You probably are going to have to "out yourself" to an employer at some point, but there is no need to do it immediately.
The issue of course is that previous employers and educational establishments know you by your "deadname". Unless you can go to all of them and convince them to always refer to you by your new name, someone at some stagethe place you apply to is going to find out about your previous name at some stage. But that doesn't have to be everybody and immediately.
I would not do this on your resume. Your resume goes to hundreds of people and is often copied all over the place. Don't put information in it that you don't want to be public. Prospective employers very rarely talk to previous employers or schools at the resume screening stage. So it's likely that nobody will do anything that reveals your previous name at this point.
The same is probably true of the interview stage. Interviewers rarely go and check previous history, and so what name you were known by won't come up. You may be unlucky, and one of your interviewers knows someone at a previous company who they talk to, who reveals that nobody named Jane Doe worked there but a John Doe did who matched the resume.
After the interview is when this will probably have to happen. You are going to have to reveal previous names for a background check or for following references. You probably want to avoid coming over as over secretive, but it is also reasonable to ask that the company only use previous names for the purpose of background check, and that they always refer to you by your preferred name. There's an argument for bringing the subject up at interview - both to make it clear you are not trying to hide your history, and also to test how the company is going to treat you. If they aren't happy about your identity then better to find it out at interview rather than after you join.