Update February 28, 2021: Dogecoin Core 1.14.3 has been released and significantly improves the synchronization speed. The method described in the original post below is no longer be necessary.
This article assumes that you have backed up your wallet and updated to the most recent version of Dogecoin Core (currently 1.14.2).
At the time of writing, you can get a torrent here which contains blocks until January 29, 2021. Note that it is not a single Bootstrap.dat file, instead it contains the blocks and chainstate directory.
You can find further information on the Dogecoin Discord (in the FAQ section), the Dogecoin Core GitHub and the Dogecoin subreddit.
Once synchronized, consider forwarding port 22556 to help the network. This should give you over a hundred connections instead of the usual 8:
This will, of course, create significant network activity as can be seen in Dogecoin Core under Help > Debug window > Network traffic. This is my traffic from just two days:
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Edit: My Dogecoin wallet on a PC that was running 24/7 still went out of sync multiple times:
Let’s not forget that Dogecoin was created as a joke.
Edit 2: I do not recommend using the full node wallet (version 1.14.2) if you’re just getting started with Dogecoin. Consider using a simple mobile wallet like Trust Wallet.