Yes, there's a small but non-zero chance.

I'd recommend first informing yourself on the difference between solo mining and pooled mining, which is mostly a payment frequency thing.

Later, you can choose to either join a pool that allows you solo mining (1 block every 15k years) or pooled mining (a few sats every day).

Here are some good pools for solo Mining: Ck Solo Mine Public Pool .io

Here are some Lightning enabled pools that accept and welcome Bitaxes: Braiins pool Ocean pool

Do check the mimum withdrawal for each pool though.

Have fun, and welcome to your latest addiction ;)