It sounds like there is some kind of problem and I'd suggest getting it checked out before shooting it. As soon as the bolt moves forward even a little, you can remove your thumb.The Mosin Nagant wasn't designed that way. Try pushing the follower down with your thumb and closing.

You can't close the bolt with the gun empty? A lot of old military bolt actions had the magazine follower designed to block the bolt after the last round was ejected.