Is it near impossible to get into rasp without OPT-40?

Anyone can volunteer for RASP, just send an email to [login to see]

Ranger Regiment accepts thousands of applicants a year to try out for RASP. They have to have a lot of applicants, 90% of them won't make it

The most important score is your PT score. You need to improve your GT score that is true but it is your PT score that you should be maxing out.
Anyone can apply for RASP the selection process is pretty simple. The Reg knows of the hundreds of applicants most are smart enough but most don’t have the physical or mental fortitude to get picked up. When you’re maxing your PT score it lets everyone know that you probably have the mental toughness to push past the pain and the physical endurance to get the job done. I can teach a monkey the skill set but the monkey has to be strong enough and mentally tough enough to carry out the mission using those skills.

It is not impossible but you have to have excellent PT scores to try and apply for it, your GT scores does not make a big difference, if you have average PT scores I advise you not to even try...