If I made a major purchase in 2019 but did not claim it, can I claim it in 2020?

[DoninGA]

No, any major purchase made in 2019 can only be entered on the 2019 tax return.

[Opus 17]

Also remember that when using the sales tax deduction, you can't actually add "major purchases"--that's a bad choice of language.  The only items you can add to the standard sales tax amount are purchases of motor vehicles, aircraft, and sales tax paid to buy or substantially improve your home.