You can certainly get self drilling screws that will zip through that with thin pan heads but generally they're for screwing into metal, I'm not sure if you can get screws like that designed for fixing into a timber substrate (ie with a coarse timber thread). But seeing as there shouldn't be too much strain on the screws I'm not sure that's an issue, Google 'Wafer Head Self-Tapping Screws'. How thick is the timber base? (plywood?)
@Harry Bloomfield using self drilling screws for fixing stuff to metal is common in the industry and you can fix (self drill into) anything up to about 12mm steel.
Or you could probably use suitable rivets with a washer on the back, if you can turn the trailer on it side to do that, unless someone is prepared to help you.
I've done a few of these over the years. Very often the original board (usually phenolic ply on a decent trailer, or some other standard board) is slightly rotted and/or quite thin (eg 15mm). I pre drill and use standard wood screws but find there's not enough "meat" in the board below and the screws come loose after a while.
I've got a new trailer to do and this time I think I'll try long rivets with washers as Freddie suggested, or thin nuts and bolts with some washers.