I am playing DnD 5e and I acquired a month old Dire wolf pup as a beast master. How long would it take for it to be combat ready? Is there a way to reduce this time?
Unfortunately, there's only one person who can give you the answers to these questions. All of this is entirely up to your DM, because you're already in pure house-rule territory.
By the rules, a Beastmaster Ranger can't have a Dire Wolf as their animal companion. There are also no rules for pups, or training animals. So, rather than asking random strangers on the Internet, you're going to have to talk to your DM about it.
The easiest way forward would be to use the normal Beastmaster rules for animal companions, use the stats of a regular wolf, and just call it a young Dire Wolf. It'll be tougher than a regular wolf anyway, so that sort of works. But even if you're going this sort of straightforward, by-the-book route, you'll still need to talk to your DM about it.
How long would it take for it to be combat ready?
A large carnivore such as a tiger or wolf typically takes about two years to become an independent adult.
Is there a way to reduce this time?
Your group can always reduce the time narratively by saying, "Two years later...."
Use the "Between Adventures" rules on page 186 of the Player's Handbook and page 127 of the Dungeon Master's Guide to determine what the PCs do during a two year montage of the pup's maturation. While you use the downtime to become proficient in Animal Handling, the other players can train their own skills or languages, build strongholds, craft magic items, and so forth.