I held down w and jumped repeatedly. Eventually after 20-30 jumps it did jump high enough to get over the first wall. I'm playing the web version in Firefox and also same results in Edge. Maybe the jump cancel is mistakenly taking effect for all jumps?
I saw you posted your code on github so I took a quick look. I don't know if this is the cause or not, but could it be that the random offsets you're applying to the player position are affecting the jump? Only reason I think it might be related is because the jump does seem to go full height sometimes, so I could see the issue being tied to a random variable.