Can you log into the TurboTax account you used for your 2017 return? If so, can you download it from there?

Did you use the Federal Free Edition (*not* IRS Free File) of TurboTax Online for any year since 2017? That edition normally does NOT include access to prior year returns; only paid and IRS Free File editions of TurboTax Online normally include access to prior year returns. (The IRS Free File version of TurboTax Online is available only thru irs.gov, taxfreedom.com or freefile.intuit.com; if you went straight to turbotax.com it's either Federal Free Edition or a paid edition.)

Also, if you used TurboTax CD/Download for ANY year, the ONLY ways you can get access to prior year returns are (a) with the prior year software and its file (.TAX), or (b) as PDF or hard copies. Intuit does NOT retain copies of returns prepared using TurboTax CD/Download, even if e-filed.

If you can't obtain your old returns via one of the ways stated above, you'll have to call the IRS or visit irs.gov to find out how to get a transcript (or sometimes a copy) of your prior year return direct from the IRS.

It is ALWAYS a good idea to save & keep PDF and/or hard copies of EVERY tax return you file as soon as you file them, whether thru TurboTax (Online or CD/Download), any other software, or manually. The only formats that won't require you to maintain old software or accounts to retrieve in future years are paper or PDF.

Yes, I can log into my 2017 account. It appears that I cannot download it because I did not file my 2019 return on that account last year. Will I be able to access it if I pay for a 2020 tax service using that account? It is saying "To download your prior year returns, just get started with your 2020 tax return in the TurboTax product that's right for you"

If you use that account with paid TurboTax (thru turbotax.com), or if you qualify for it the IRS Free File version (thru freefile.intuit.com), you should have access to your prior year returns; at least that's how it's been done in prior years. Note that IRS Free File does not have many of the value-added features of turbotax.com, such as Refund Advance. Also, you may not be able to import your 2019 numbers into your 2020 return if you use a different TurboTax account for 2020. (TurboTax staff, please chime in if you have any additional info.)