Yes there is, although it's rare

Here is what I'd do if I were you:

Build a list of all the companies you could/want to work for

Build a list of all the linkedin profiles of their HR/recruiters/talents or (co)founders for small startups(you can use phantombuster or a custom puppeteer scraper)

Find all their emails using wiza, dropcontact or a similar tool

Use a mailbox warmer for a few days/weeks to prepare your mail address to send lots of mails without getting flagged as spam

BCC all of them asking if they'd be open to hiring part-time (or use lemlist)

you can also send automated linkedin invites/messages to them