I did think about screwing from below as in Homer's post above.
It's the obvious way to go, but what put me off was the thickness of the boards.
I guessed they looked around 20mm. A screw going about 15mm into the boards from underneath would hold, but only as long as the timber doesn't try to warp and "curl".
I would be much happier screwing down from the top.
I'd use these...
https://www.screwfix.com/p/quicksilver-pz-double-countersunk-woodscrews-6-x-2-200-pack/13733
(In France - the metric equivalent would be 3.5 x 50mm)
3.5 size has quite a small head.
With your new cordless screwdriver... lean on the driver with both hands and let it drive the head of the screw right into the timber, so that the head of the screw lies about 5mm below the surface.
Then...
I guess there are all kinds of brown fillers around, but I just use something like this...
Amazon.com User Recommendation
If you run a small sander (I use a "palm" sander) over it afterwards, you'd be surprised at how the holes can be less obvious.
One thing... pre-drill the timber for each screw. Although these screws say that no "pilot" hole is necessary, I disagree. The screw goes in a lot easier, and more accurately with a pilot hole.
In a previous post I said 3mm holes. That was a mistake... use 4mm holes with these screws.