As simply put
Cap creates his own time loop that ends with him aging himself out
So the entire movie run sees him go back in time to possibly when he was frozen and gone and he lives his life as an old man with Peggy. The cap we known still gets unfrozen and does everything he’s done in the movies but he ends up going back in time to live his life with Peggy and get old. He manages to still do everything he’s done and still live his life with Peggy until she gets Alzheimer’s pretty much. Maybe he secretly changes his name or he just stays hiding while married to her all that time so he doesn’t mess with time too much but yeah
That’s still his shield he has and he gives it to Sam maybe it gets fixed after the fight before he goes back or maybe it’s a shield from back then idk but it makes some sense. Plus he changes the past anyway when he stills the pym particles and directly causes hank and tony to beef back in the day and sets forth that trajectory
everything in the that final battle flowed together damn near perfectly whether you liked it or not then you're just sitting there like" wait ..... is that..... everyone? or .... oh 
its one of those forced moves again. okay. is that box checked now? cool. back to the movie"
no wonder he got his ass handed to him by Thanos.
when BP showed up. My Black ass damn near hopped out the seat entirely:
Plus we act like ant man can't survive explosions... and war machine WASN'T in his suit when him, banner and rocket fell into the crevasse... 