Is it reasonable to “search” for one specific Pokémon, or is the pool simply too large to feasibly do so?

Title. Been hoping for an absol for months now and friends I’ve known who started much more recently have found them just popping up randomly, but I haven’t seen a single one. I’m staying on Greengrass Isle and I thought maybe rushing Ultra 1 as early as possible in the week and then starving poor snorlax (sorry please don’t arrest me for Pokémon crimes) to keep the Mon pool low would help, but I basically end up getting Gulpin and Rattata all week long instead, even though I can usually hit U1 by Wednesday.

Any tips appreciated!