After some testing I realized the RNG factor doesn't really exist. All items for all the holes are decided before the game starts, so when you start the run, you can already know if you'll get a skip item on the first level.

By default, if you boot the game and play it for the first time, you won't get the skip on any hole (The first item will be a shield behind you). If you either die or complete the game, when you start again new items will appear. If you boot up the game again then the first version will appear again. Apparently the set of items depends on where you die (or if you complete the game), also depending on the version you got before. That would be the only random thing in the game since you have to find the perfect "version".

In my case, I found that by getting a game over at the first water zone of Hole 8, during a "First version playthrough", I would then get a version that has a skip on Hole 5. Upon realizing this I saved a state and now I don't depend on the spawns anymore. Anytime I choke the run I just load the state and I can still get the skip on Hole 5.

Hopefully this isn't very confusing, but if anybody wants to try to aim for this run in the future, I'll be glad to explain it more clearly. This is the route I found, and although it has a skip, it doesn't have any 1ups or Health boxes, so it's actually a lot harder to get through. I'm sure that if you experiment enough there might be other versions with better set of items, maybe more skips, or more convenient ones.