As a former Marine looking to join the Army as a 37F, how could I get sent to RASP after my MOS training is complete?

You can attend RASP at any time. Option 40 is a recruiting tool meant to sucker young wannabe Hooahs into joining the Army. 90% of them fail and end up in the Regular Army, so it's a very successful tool for the Army to recruit to fill the Infantry.

You can apply to attend RASP right as you finish your AIT, but your MOS training is not going to be very physically challenging. Psyops (MISO now) is like the special operations version of public affairs with a foreign language thrown in there. When you get to the MISO there will be a tactical group that gets attached to the SF and Rangers. Chances are you won't want to suffer through RASP and earn your Beret and scroll when you can just be attached to them.

Theres like 4 positions for 37F at regiment, and they dont put brand new Psyoppers there. Only very experienced and tabbed 37Fs

This depends on whether you are Active or Reserves component. I was Active PSYOP until recently, now in a Reserve PSYOP unit. When I graduated the Q-course for PSYOP back in 2015, everyone was offered the option to attend Ranger School before going to their respective unit. Especially if you go to 9th BN (assuming you are on Active Duty and not the Reserves), they will constantly ask you to build your packet to go to Ranger School (not RASP, though you can put in a packet for that as well) as they ultimately want you to be Ranger-qualified. It's not as much of a priority in the regional BN's, but you will be offered the opportunity to go while there as well, assuming you're in a window where you aren't scheduled to deploy. The Active Duty side of PSYOP has lots of funding for training and many of the best schools will be open to you. Reserves, you'll probably get Airborne and training opportunities will be few, limited and far between beyond that.