Will inventory likely increase in the next couple of months? Looking for a studio <$2,300 in Manhattan/Brooklyn/Queens but majorly struggling

I know I can't be picky with my budget (max $2300/month), but I'm shocked by how low inventory seems to be - I'm looking at a ton of different neighborhoods throughout Manhattan, Brooklyn, and Queens, but the only listings within my price range are scams. I'm even okay with having a micro studio and sharing a bathroom with other units, but I'm literally just not finding anything on Streeteasy. I've tried looking on Craigslist but have only come across shady listings so far - should I be trying harder on Craigslist, waiting until inventory (hopefully) increases in the summer, or trying something else entirely? I've heard that bidding wars get crazy over the summer, so I'm not sure if waiting would be worth it even if inventory goes up then.

I am from out of state and would ideally like to move by early July but could delay until late August if I needed to. I have a pet that does not get along with other people, so living alone is a priority for me. Any insight or advice would be appreciated <3