Is there a way to amend my 2022 return to include an IRA RMD without a 1099-R form or should I wait until I file my 2023 return?

you have to file 2022 Form 5329 when you miss an RMD.

The proper way to file Form 5329 is attached to Form 1040-X.
Form 5329 can be mailed by itself only when you are otherwise not required to file a tax return.

After you e-File,
get Form 1040-X from IRS website and mail it in with your 5329 which you can also get in fillable PDF.
Note: assuming you request a waiver of penalty, since you are not changing any dollar amounts on your amended tax return, you can leave all the lines 1-23 EMPTY.

Part III explanation: will explain to the IRS why you missed the RMD, what action you took that they should waive your penalty. This is required if you request a waiver.

@mithmc 

You will have to mail it so this does not use up your one 1040-X e-File.
Done this way, you sign 1040-X, not 5329

This distribution received in 2023 is 2023 income reportable on your 2023 tax return.  As fanfare said, you must file 2022 From 5329 to request a waiver of the excess accumulation penalty.  See the instructions for Form 5329  Part IX regarding a request for waiver of the penalty.