If I didn’t finish filing my taxes with TurboTax can I file it with H&R Block instead?

If you have not paid any of the TurboTax account fees with a credit card, then you can clear the tax return and close the TurboTax window on your browser.  Then you can use whomever you want to assist you with your tax return.

If you have not paid for the online edition you are using, have not filed your tax return or registered the Free edition, then you can clear your return. Click on Tax Tools on the left side of the program screen while working on the 2023 online tax return. Click on Clear & Start Over.

If you have not e-filed, yes, you can go somewhere else.  If you already e-filed, no, because you cannot file twice.