i am a dual citizen with 2 different DOB due to a old mistake happened (nope cant fix now)

i will be traveling to the US i am a us/jordanian citizen i live in saudi arabia at the moment (with my jordanian passport as a resident) i am looking to go to the US but i cant book a direct flight because airlines will need verification and im afraid they ask to see my us passport and notice 2 dob?? what shall i do in this case? i was thinking to go to a country which doesnt require visa for my 2 citizenships such as Egypt leave saudi with my jor passport and as soon as i arrive to egypt just pull my us passport.. will that work? will they ask? then from egypt to the US..

also i have never been to the US since i became a us citizen my passport is empty of stamps will that cause a problem in the US or egypt?

thanks, appreciate any help.