Bugsnax is one of those types of games that you wish you could change the weather on a whim, but you cannot. The weather is in the fate of the Bugsnax gods; just hope you get lucky and get the watery goodness from the sky. Though there is a way to increase the chances of it raining, this is just a faster way of waiting.
Bugsnax How to Make it Rain
Sadly in Bugsnax, you cannot make it rain manually, but there is a way to make it rain faster by sleeping your days away in Snaxburg. Skipping days does not alter anything in the game, so sleep until you get rain!
As there are 100 Bugsnax to capture on Snaktooth island, there's a lot to keep you busy. However, the main element of Bugsnax is figuring out the ways to capture every one of them, as each one requires a different approach. This could be as easy as finding the correct sauce they like. For example, a Bunger loves Ketchup, or a Sandopede adores Salad Dressing!
Once you progress deeper into the game, the ways you can capture bugs becomes more like Pokémon in a sense - that some only come out at night, some only come out during different weather types, such as rain. Raining can happen whenever; it's completely random, so waiting for the day that it rains can become a tiresome chore, especially if the last of the Bugsnax you require only appear when it rains.
There is a way to get rain to happen faster, and that is by heading back to Snaxburg and sleeping until it starts to rain. This is the best solution you have in the game to get the desired weather you want! All quests and side quests will hang around regardless of how many days you waste by sleeping, so zzz away!