For example, I completed my CPL multi and have 300 flight hours, can I do a A320 type rating and work for an airline if they allowed my to work with 300 hours?
A U.S. pilot with a Commercial license can get a type rating by going through an appropriate course. It isn't cheap, but it can be done.
The benefit of having the type rating with only 300 hours is probably pretty slight, at least in the U.S. Anybody hiring into the right seat of an A320 either has their own "ab initio" curriculum, or else they're probably looking for far more experience than that. There may be a unique job out there that is looking for exactly this sort of applicant, but it seems hard to imagine.
You might be better off saving the money until you have a line on exactly what position you're after, and you're confident that they'd hire you with 300 hours (or whatever you have by then). Who knows -- you may find someplace that will be glad to hire you to fly something else, if you'll get the training on (whatever they fly) by going to get the type rating. Having the money available to spend on the needed type rating could be a lot more useful than have the 320 type at that point.
This is actually 2 different questions (at least here in the US it is)
For example, I completed my CPL multi and have 300 flight hours, can I do a A320 type rating?
Yes you can get a type rating in any aircraft you please provided you can deal with all the requirements to do so.
and work for an airline if they allowed my to work with 300 hours?
Generally speaking no, it seems like you are asking about what is called part 121 operations here in the US. For that you will need an ATP ticket which requires 1500 hours of flight time. You may however be able to fly for a charter airline (operated under 135 regulations) but you will need to find one that is flying A320's....