Why did Michael wait a year after returning to the US to contact Kay and propose marriage? Your thoughts?

Well, in the book he's busy during this period, learning about Vito's business holdings and political connections.

Good Question. Like mustache says he was busy learning more about the family at the same time start to take over the reigns

Yes, Michael would have been joined at the hip with Vito for at least a year--no time for distractions like romance, marriage, starting a family.

But, I believe Michael also would have had to give a lot of thought to where Kay would fit into his new life. He would have had to be certain that he put Apollonia,the "thunderbolt," and her tragic murder behind him. He also had to figure out what he would have to tell Kay, and adjust in his own plans, for her to accept him in his new role. And, calculating manipulator that he was, he had to form a good idea of how he would use her to help "legitimize" himself--his obsession.

In movies, we often see marriage proposal scenes where the guy drops to one knee and begs the gal to marry him. That scene in New Hampshire, with Michael, dressed like a pint-sized banker in that ridiculous Homburg hat and his carefully rehearsed speech, looked and sounded much more like a merger/acquisition negotiation. .half-expected Tom to jump out of the limo and hand Kay a contract to sign, with clauses and exceptions, and stamp it with a Notary seal.

If you mean? for Michael to use Kay's WASP “to help "legitimize" himself--his obsession”....
Kay was already Michael's girlfriend, long before Michael having to become the Don and his quest for "legitimacy" "respectability"

• Michael was honest though

I came here because I need a woman, to bring my sons into this world. You'll do -- What's Love got to Do with it?!

Michael had no qualms marrying Apollonia and took longer than a year to contact Kay -- Mama couldn't find Michael a nice Italian origin bride, suitable Mob Boss wife! instead of seeking Kay out