Can I file returns for past years for the first time, as these need to be new returns not amended returns?

You cannot change the tax year.   The current online program is for 2023 only.   Only a 2023 return can be prepared online and only a 2023 return can be e-filed.

Online preparation and e-filing for 2020, 2021, and  2022 is permanently closed.

To file a return for a prior tax year

 If you need to prepare a return for 2020, 2021, or 2022  you can purchase and download desktop software to do it, then print, sign,  and mail the return(s)

https://turbotax.intuit.com/personal-taxes/past-years-products/

You may also want to explore purchasing the software from various retailers such as Amazon, Costco, Best Buy, Walmart, Sam’s, etc.

Remember to prepare your state return as well—if you live in a state that has a state income tax.

https://ttlc.intuit.com/community/state-taxes/help/how-do-i-contact-my-state-department-of-revenue/00/25573 

When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s.  Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS/state received the return.

Federal and state returns must be in separate envelopes and they are mailed to different addresses.  Read the mailing instructions that print with your tax return carefully so you mail them to the right addresses.

Note:  The desktop software you need to prepare the prior year return must be installed/downloaded to a full PC or Mac.  It cannot be used on a mobile device.

Yes for the last 3 years.  

Online is only good for the current year.   You can buy the last 3 years of Turbo Tax here,

https://turbotax.intuit.com/personal-taxes/past-years-products/

You will need a full Windows or Mac to install it on.

How to prepare a prior year return

https://ttlc.intuit.com/community/using-turbotax/help/how-do-i-prepare-a-prior-year-tax-return/00/25984

You will have to print and mail in prior year returns.  And if you are doing more than 1 year, send each year in a separate envelope. Sometimes the IRS will just staple all the sheets together and miss a second return.  Be sure to attach copies of your W2s and any 1099s that have withholding on them.  Don't forget state.  You have to mail federal and state in separate envelopes because they go to different places.  Get a tracking number from the post office when you mail them for proof of filing.

Or if you want to file for free and have a simple return you can get the blank forms from the IRS and fill them in by hand.  I have a list of some of the basic ones I can post direct links to.

To complete and file a prior year (2022 thru 2020) tax return using TurboTax you would need to purchase, download and install on a personal computer one of the desktop editions for each tax year required from this website - https://turbotax.intuit.com/personal-taxes/past-years-products/

A prior year tax return can only be printed and mailed, it cannot be e-filed using TurboTax.

When mailing multiple tax years use a separate envelope for each tax year.  Also use a tracking service from the UP Post Office when mailing so that you will have proof the IRS received the tax return.