If I control Sheltering Ancient and it's equipped with Assault Suit, will it's comulative upkeep happen when I give an opponent Sheltering Ancient on their upkeep?
No, it won’t.
At the beginning of each opponent’s upkeep, only Assault Suit will trigger. When the trigger resolves, you can give Sheltering Ancient to that player until end of turn. Since that opponent didn’t control Sheltering Ancient when their upkeep began, it’s too late for the Cumulative Upkeep ability to trigger.
Even if it could trigger, your opponent could just choose not to pay the cumulative upkeep with no downside. You couldn’t force them to pay the cost.
Cumulative Upkeep [cost] means “At the beginning of your upkeep, if this permanent is on the battlefield, put an age counter on this permanent. Then you may pay [cost] for each age counter on it. If you don’t, sacrifice it.” You can still choose to not pay cumulative upkeep even if the creature is equipped with Assault Suit since sacrificing for CU is a default action not a positive choice that can be made. So on your turn when the Cumulative Upkeep trigger resolves, you can just choose to not pay, then the creature tries to sacrifice itself but Assault Suit prevents the sacrifice.
