In my opinion, the aged Captain America we see at the end of Endgame has lived within the same timeline, despite the many theories to the contrary that say his choices led him to an alternate timeline. The fact that he appears/sits on the park bench is significant here - if he were part of an alternate timeline then there would be no guarantees the group would be gathered at the same time and place, and if he wanted to return to the original timeline from a different one then he would have used the Pym particles to make sure. The only way he could be there at exactly the right time is if the events of the timeline were the same. The fact that he didn't come back using the machine Tony had created seems to confirm this theory, meaning that Cap simply aged within the original timeline. 

But how can that be? Surely by remaining in the past he has inherently altered the timeline? Perhaps not.

We are thinking of the timeline as exactly that - a line - but for Cap it's more like a loop. If Steve's future was always in the past, then him existing in the past wouldn't change the timeline of events (stay with me here). If in every timeline, Captain America goes back in time to live in the past, then he has always existed in the past and the younger Cap's timeline would remain unchanged. 

I hate time travel. This is The Prisoner of Azkaban all over again.

We don't know for sure when Cap went back to and there are many theories on this, but I personally think he went to the 1970s to return the Space stone and simply stayed there. When he and Tony go to the 1970s to find the stone initially, he sees the love of his life, Peggy Carter;  I think the presence of Peggy is again significant, and although he could have gone to any time in the past, it would make far more sense if he stayed in the 70s when returning the stone to its original timeline. Cap goes back to be with Peggy after defeating Thanos in the year 2023 which makes the age difference between him and Peggy in the 1970s almost negligible, compared to if he returned to the 1940s (although there are questions about how Cap's ageing works).

It's also unclear how many Pym particles he would have left, so he may not have been able to go farther back even if he wanted to. That said, we do know Pym particles existed at that army base since Steve and Tony got their extra supply from there, so perhaps he did then move on to the 40s after dropping off the Space stone. You would think after a theft as brazen as Tony and Steve's however, that security would have been significantly increased. Like...a lot.

This time trip also raises the questions of Peggy's husband and there are theories that suggest that Steve was the husband all along. This makes sense if he did in fact return to the 40s after replacing the Space stone, but not if he only went as far as the 70s. We know that in an interview in 1953 Peggy references a husband that was saved by Captain America - some people believe this is a cover story for Steve, but this can't be true if he stayed in the 70s. I think Peggy was married to a soldier, and that by the time the 70s rolled round, he was out of the picture (it's not unlikely for a soldier back then to have died in combat or experienced a relationship breakdown). It's also likely that 30 years after Captain America disappeared he would be less readily recognised by people who have assumed he is long dead, thus allowing the timeline to stay uninterrupted and not have people question how Captain America aged and then was found in ice so many years later, young again. Steve Rodgers is the kind of man that would always get involved in a situation if he thought it would help someone, so it seems almost impossible that he would be able to lay low in the 1940s given how famous he was. 

If you want some extra heartbreak, Peggy died in 2016 which means Old Man Logan Cap has been widowed for 7 years by the time we see him in Avengers:Endgame. Sorry.

That kiss in Captain America: Civil  War is even weirder now than it was before. Like...did she know she was kissing her great UNCLE? I know they aren't blood related but still, that's a little messed up, right? Captain America couldn't know then that he would go to the past and marry Peggy, so he wouldn't know Sharon was family (by marriage or otherwise) but you'd expect family members to have grown up with pictures if not personally meeting Peggy's husband?

The fact that Sharon clearly doesn't know adds weight to my personal opinion that Cap either assumed a new identity (which due to Cap's fame in the 1940s suggests he was in a different decade where he was less well known and recognised (i.e. the 1970s)) or at least kept the relationship fairly quiet. 

Now that we know there is a version of Captain America in the past when we assumed he was a Capsicle,  is there a potential we will see some crossover with him and Captain Marvel? It's unlikely that we will ever see a reprisal of the Cap we know, especially with that emotional handing over of the mantle to Sam, but it would be cool to see a cameo or a reference to Steve's life with Peggy, if only to clear up some of these questions and theories!