I forgot about the federal tax credit for solar on my 2021 return. The system was installed and went live by November 3, 2021. Can I amend my return and include it?

Yes, you can amend your tax return once it's been filed and accepted. Please see this TurboTax FAQ here for assistance.

In lieu of an amendment, can I just wait until next year to get the tax credit or do I have to apply for it for the same year of the installation?

sadly it is the year of installation.... wait at least a month though before filing an amended return as the IRS is backlogged. Good luck.  I don't work for tt.

Hope I was helpful.

Very helpful. Thank you.