I did not file 2021 taxes. Should I complete 2022 first or 2021?

It does not matter unless you had some type of carryover on the 2021 tax return.  Then you need to complete the 2021 return before fling the 2022 return.

To complete and file a 2021 tax return using TurboTax you would need to purchase, download and install on a personal computer one of the 2021 desktop editions from this website - https://turbotax.intuit.com/personal-taxes/past-years-products/

A 2021 tax return can only be printed and mailed, it cannot be e-filed.

Ideally, you should look at filing an extension for 2022, and completing your 2021 first. That way, if you have any carryover credits etc, you can apply them in 2022. You can also file your 2022, and then amend any changes that may arise from adjustments to 2021.