The best way by far is to just use load of stone and try to keep it eating a all times. I tried stone structure for a level 145 and I made 36 structures and it only went up 7 percent. I used a ton of stone for the same gacha and it tamed in under 5 minutes (don't drop them one by one)
If you are wanting to tame with the snow owl. You can use the owl’s secondary attack to freeze the owl and use up the stamina. This will force it to eat more and will produce the pellets for taming the gatcha. It also works well once you have it to get higher quality crystal drops from it. Just put the owl in front of the gatcha and then when the owl drops pellets the gatcha will pick it up automatically.