Musk might deny it for basically every year from 2008 up to when Bitcoin reached some level of success, for the integrity of the currency, and to avoid entanglement with aggressive regulators who don't understand the possibilities for good (see the fate of the E-gold founder) (luckily the atmosphere has changed with Vitalik Buterin publicly inventing Ethereum and Billy Markus publicly inventing Dogecoin). Let's say that from 2008-2013 (2013 is the release date of Dogecoin) there was sufficient reason to deny.

Then onwards, Musk might continue denying because priorities are SpaceX and Tesla. This reason might essentially continue on to the present. So this explains the range 2013-2022.

Now in the present, what can change the situation is sufficient public knowledge that Musk invented Bitcoin and sufficient public will that asks Musk to take credit, with the understanding that taking credit for Bitcoin will unify the positive perception of Satoshi with Musk, and accelerate time to civ on Mars.

The evidence is now beyond reasonable doubt that Musk invented Bitcoin. Capability. Motivation. Linguistics. Plus the extraordinarily specific commonalities. C++ proficiency. Location in Van Nuys, Los Angeles. Fulfilling the Exact Paypal Dream.

For a quick rebuttal of the other candidates, Nick Szabo doesn't seem to code in C++, Len Sassaman was sincerely dismissive of Bitcoin, Hal Finney was not playing games emailing himself, and Craig Wright is what you say he is.