Unprepared for the NYC marathon

Been looking forward to running the NYC marathon after finishing my 9+1 last year. But earlier this year in May, I got an Achilles injury from a run. Fast forward to today, it doesn’t hurt anymore when I walk normally but when I strengthen train and/or run, it’ll hurt a little the day after.

This is my first ever Achilles injury so I’m not sure how long it’ll take to fully recovery. Didn’t go to PT (could use some recommendations)

I now realized that I have less than 3 months to train for the marathon. I don’t want to defer it since I’m doing the 9+1 this year again to qualify for next year.

This is my first ever marathon so I’m not looking to complete it in a specific time. But do yall think it’s doable to train a little (2-3x a week maybe) and complete the marathon? Anyone in the same situation feeling skeptical?