Oh your question... what psi? Lets look at the map
Looks like compressor outlet pressure of at least 1.8 pressure ratio will be desirable... so a minimum of 11.6psi off the compressor is a starting point.
Then we factor in pressure drop. Compressor wheel is a PUMP just like any pump it will produce what engineers call 'pump head' and everything after the compressor will take a chunk of that head, so for example, the bends in the pipe, the roughness of the pipe, the volume and length of the pipe, the intercooler, the throttle valve, the intake port/shape/design, the head/valve, all of that is considered an obstacle to the pump head and will reduce the effective flow and pressure of the turbocharger outlet.
To put it another way, everything after the compressor will cost power. That includes the bends, pipes, even the intercooler, all of those items will reduce pump head and therefore impose limitations to compressor flow rate downstream of the wheel.
Luckily the math is easy and quick to estimate... you don't need to think that hard. Just over estimate (use a conservative outlook)
If the compressor jams out 12psi and we lose 2 or 3psi from the pipes and intercooler etc... that leaves our intake manifold pressure at 9 or 10psi of boost pressure.
Looking back at the map, 12psi at the compressor wheel is good for maybe 37lb/min max flow rate. Minus mileage, friction, wear and tear, time, (being conservative) lets call it 35lb/min down the road and for the sake of reality is a max flow rate of that compressor near 12psi of outlet pressure (9 or 10psi intake manifold pressure).
35lb/min at reasonable temperature with typical gasoline fuels will net roughly 350bhp or around 300rwhp, maybe 290rwhp or 310rwhp, you know its not exact.
Now lets consider the engine displacement and see if these compressor goals match our engine flow rate,
2L Is 122 cubic inches so,
122*7000rpm/3456 = 247CFM
Now add boost and assume 95% Volumetric efficiency at 7000rpm,
Take out 5% VE: 247 * .95 = 234CFM
Add 12psi of boost to the intake manifold: (12/14.5) * 234CFM + 234CFM = 427CFM
Converter CFM to MASS by using typical air temperature conversion: 427CFM * .078 = 33.3lb/min
converter lb/min to bhp: 330bhp
converter bhp to rwhp (assume 12% drivetrain loss): 333 * .88 = 290rwhp
*note the constant I chose as .078 could be typical-anywhere from .068 or .085 depending on the air temperature which is reflected in the density of air. This is where it is critical to defer volume rate to mass flow rate.
Also Note that VE I chose at 95% could easily be 90% or 105% depending on the head and cam selection.
A stock camshaft at 6000 or 7000rpm would also be more near 70% or 80% perhaps.
So to answer your question with a 95% to 98% confidence interval of approaching 300rwhp using the posted compressor map, even in the face of reality, time, friction, usage, plumbing/piping/intercooling head loss, inefficient this and thats, you should see 11 to 13psi compressor outlet PRESSURE and approx 9 to 11 intake manifold PRESSURE to achieve your desired flow rate of 35lb/min (300rwhp) from a dynojet as a maximum output from that compressor wheel according to the map, using typical gasoline fuel and typical temperature (70-90*F Ambient & post intercooled w/ gasoline)
If the engine has a cam upgrade which can achieve at least 95% VE at those posted RPM.
Couple caveats.
1. the compressor maps often more conservative than reality so some of those turbos might support more power than the map claims
2. Temperature has a massive effect, lower IAT can dramatically change the compressor wheel mass flow rate. This is because the compressor does not flow MASS it flows VOLUME rate, the reason the map is presented to us in MASS rate is because they have taken the liberty of assuming some specific temperature in their volume flow rate calculation which was then used to convert the map into a MASS rate for people to quickly tell at a glance what sort of power to expect. So you MUST consider that original temperature they used as a constant (and it is NEVER constant Temp in reality) when you are examining those compressor maps in terms of MASS flow rate.
For reference, The typical mass rate conversion is done using approx 90*F iirc air temperature, or something near that.
So for example if the ambient temp drops into the 50*F or something low like that, it will dramatically affect compressor mass-rate.
3. The compressor can only flow some volume rate as discussed in #2, but the caveat on top of that caveat is the fact that any air molecules LOST downstream of the compressor will cause imbalance of compressor/exhaust flow rate, the demand of the exhaust wheel is increasing based on however many air molecules are lost from the compressor. In other words, #3 says that if you are leaking boost, the exhaust gas pressure AND temperature will rapidly rise and destroy the engine. Thus you MUST ENSURE there are no boost leaks. You MUST PRESSURE TEST the entire system from the compressor wheel to the engine before running boost pressure or you WILL probably Destroy the engine.
4. Stock exhaust... and stock cam will both limit engine VE severely. SO many more intake manifold pressure (PSI) will be required to achieve these numbers. I would say 20% to 35% extra PSI to achieve the same rwhp using those stock components. Figure 18psi or 22psi might be required.
Luckily, pressure in PSI at the intake manifold is not so important... for a few reasons.
A. the intake and head on these engines is made of metal, so high Pressure cannot explode those parts (like an LS1 intake manifold would)
B. 15psi or 18psi or 22psi is negligible compared to the 800psi or 1000psi of combustion pressure... so it does NOT reflect in the reliability of the engine's internals, the fuel quality cares only about the TEMPERATURE and ultimate COMPRESSION (800psi~), not the 'beginning pressure' of 20 or 30psi or whatever.
C. The compressor map dictates efficiency and we can see that after 12+ PSI of outlet pressure, the efficiency only gets better and better. SO in reality we are better off using MORE pressure in PSI, as required or as by engine flow rate allows.
D. The intercooler ability to cool air is more dependent on the total mass of air rather than the volume. In other words, if the engine VE suffers and more PSI of boost is required, the outlet temp of the compressor is increasing rapidly, however an intercooler can effectively cool the same mass-rate of air similarly, reduced density due to high air temp means a larger volume of airflow per unit time, as each molecule of air is more spread apart from it's partners the (heat) energy may be more effectively extracted per unit volume as well (it is faster and easier to cool a high temp low density air volume than it is to cool a very dense high temp air volume, i.e. pressure does NOT directly control density by itself). Thus we may rate intercoolers in terms of 'potential power' and their pressure drops as 'potential volume flow rate' separately. So while pressure drop is increasing with additional volume flow rate of expanded air due to high temperature input, our compressor potential flow rate always has the final say in whether that pressure drop influence can limit engine power... up until, of course, some physical law limitation such as the velocity of air approaching the speed of sound for example, or at the influence of turbulence.