Dogecoin was created on December 2013, almost 8 years ago, by two software engineers Billy Markus and Jackson Palmer
In those days, they did not think Dogecoin would have been popular but mostly a joke, therefore they did not propose any airdrop, ICO or pre-mined coin. With the idea of trying their mining process, even though Dogecoin mining difficulty is not the hardest one, after five minutes of mining on Billy Markus' gaming computer the difficulty was too hard to be worth to continue. By being the only one mining on the network, as I understood, they mined for about 5,000 $ worth of Dogecoin together and they never held more of them.
Therefore, Dogecoin is one of the crypto assets which has no supply limit. Currently, according to Coingecko, and CoinMarketCap, there are 129,680,464,638 of DOGE in circulation. We can say that, with no cap reachable, mining could be possible until the death of the coin (if it dies ).
Even this story highlights the full joke of the project! By mistake, they thought putting a 100,000,000,000 supply limit for the coin, by changing some lines in the code they recycled, would work to regulate the supply limit, but it was not that simple