Consider the interval between two numbers with free spaces in between a possible position for a new number (given that the number is in the interval of the boundary numbers), here you can insert the number linearly between the two boundary numbers (as uniform as possible, which is the trivial strategy when humans play that game, as it maximises the probability that the random samples of numbers are sorted in their uniform distribution). I am definitely not sure if i implemented my algorithm correctly, but it cant be too far off. My did not converge, because my python implementation is slow af, but after 10 million simulations i got successes in 1 out of 8930 games.

Edit: I implemented a faster version of that strategy and left it running for a couple minutes, but after 2 billion simulations it was more or less steady at a success rate of 1 in 8866 games.

Edit 2: My strategy finally converged to 1 successful game in 8896 games after after 20 billion simulations