I understand that if you earned less than 600$ in the tax year they aren't required to send you a tax form. So I'm kind of lost on if I need to file at all or if I do, what form do I need to use?
If you don't have other income you are not required to file. You might choose to do that anyway, and you can start with TurboTax Basis and upgrade later, if needed. TurboTax Free Edition
I have 2 other W-2 forms that I am filing for 2020. But I did DoorDash on the side towards the end of the year and it was my only side gig.
You still can start with the free edition. You might not need to claim your expenses for Door Dash gig, since your income was only $300. You can report it as Other income. To do it in TurboTax follow these steps: