Can you get buffed random matches more often?

As far as the mode goes, there usually is not a player-side way to force it more often. It tends to be a rotation thing, so some days you’ll see it pop up a lot and other days not much at all.

Tier can matter for some special battle types in general, but the better explanation here is usually that the mode is only active in the random queue during certain windows or under certain matchmaking rules. If you are only seeing it once a day, that can still be normal.

If you mean the random battle variant with map buffs, that is just the arms race version. It is not something you unlock by playing a certain tier, at least not in the simple way people sometimes expect.

The main thing to check is whether the mode is currently active in the random queue for your region and time. When it is available, you get it based on matchmaking, not because you did anything special. So the short answer is no, there usually is not a reliable way to increase the odds from your end.

I would treat it like an occasional queue flavor rather than a separate mode you can farm. If you want it more often, the only practical thing is to play when more people are online, since that can affect how often you land in whatever special rotation is live.

But there is no clean tier trick I know of. If anything, you are probably just getting unlucky with the timing.