Is it possible that the Bitcoin creator (or developers) have an algorithm that allows computers to generate coins easily, but intentionally published only the current difficult mining algorithms. And, in that way, have left themselves a backdoor way of generating bitcoins once the algorithm became popular?
Your question is equivalent to asking, "Does SHA256d have a trapdoor?"
SHA256d is a well studied algorithm. It's believed not to have a trapdoor.
If the creator of bitcoin has a way to break SHA256d, stealing all our bitcoins would be the least of our worries.
Basically, yes. But it doesn't have any dramatic effect and it's almost certainly over by now.
When Bitcoin was first released, it was not generally known that it was possible to mine efficiently using GPUs (video cards). It's possible that the Bitcoin creators and early developers knew this and withheld the information, giving them a tremendous mining advantage if Bitcoins had gone up in value before this was discovered by the general public.
Note that you can't mine "more" Bitcoins in total this way. Bitcoin's core mechanisms limit the total number of Bitcoins that will ever exist to a bit less than 21 million. But you get a much greater share of the Bitcoins mined than you would otherwise be entitled to.
Since the announcement of Bitcoin and since the value has gone up, the mining algorithms have been very well studied. Any such creator advantage would long have dissipated now. Bitcoin didn't pick an algorithm that's fundamentally new, the difficulty of mining is based on the number of SHA256 hashes you have to do and it's almost inconceivable that there would be any faster way of mining other than figuring out how to do these hashes as quickly as possible.
There's no secret backdoor. There's simply no place to hide one. But it's possible the developers had a head start on figuring out how to execute the mining algorithm quickly. Again, that's long since dissipated. The mining community in general has now had a massive resource advantage over anything the original creators and early developers could have mustered. They wouldn't have invested millions into the fastest way to mine because that would have been an insane risk before they knew Bitcoin would even catch on or that the mining algorithm would remain the same.