How do I recover deleted email from Apple Mail using Time Machine?

A deleted mail has been removed when emptying the Bin of Mail by Apple (Ventura 13.7.4 ) Now I try to find this sent or removed mail . A search with the Time Machine was not succesfull, I encountered that not all software programs can handle my problem. Proably because my Imac is too old. Which free software will you advice me to recover the old mail,which I am interested in. Thanks

.

With kind regards

R.KINGET

[Re-Titled by Moderator]