To account for the fact a muse from the 1940's is going to be interacting with all sorts of muses and creating probably wrinkles in the fabric of the time-space continuum, here's the
A Stark Did It version of why he's interacting with your muse.
After WWII, Howard became obsessed with Cosmic Cube. Power like that needed to be studied. If the tiniest portion could produce weapons of destruction, what else could it do? He began experimenting, admittedly even by his own standards, recklessly so. The ray he invented was supposed to just teleport people. If all forms of travel could be rendered obsolete and replaced solely with one uniform mode of transportation, he'd be up there with Edison and Bell. All the preliminary tests went well. The guniea pigs, dogs, sheep, and chimpanzees all ended up fine and still containing all of their major organs. One test left. A human being. It was a simple test. Teleport from one end of the lab to the other.
Dame Fate, however, chose that moment to be a fickle bitch. A power surge in the lab caused the ray to blast Howard with twice the amount of power. The next thing he knew, he was standing on the other side of his lab......falling apart and with decades worth of dust coating the windows. What would you do, stranded seventy years from home, with no way to get back?
A) Have a mental breakdown.
B) Angst about suddenly being cut off from all your loved ones.
C) Run around like a kid in a candy store and start experimenting with all the future tech you can get your hands on.
No prizes for guessing which one Howard chose. Sure, he'll need to find a way to get home eventually. There's that whole stable time loop thing in place to make sure Tony gets born and that everything proceeds according to what happened in Iron Man 2 and all. But what's the rush? He's got all the time in the world.