Fly press would do that, and modify the holes as required......

I think the tool used to do this manually is called a 'dimple die'.

It might be wise to find out the standard sizes in which these are available and size your holes to suit.

Then you can use a standard commercial laser cutter for the sheet and form the dimples yourself.

Nominal 14mm (9/16") or 16mm (5/8") may be cheaper than 15mm because a lot of auto-body fabrication uses imperial.

For a one-off I'd think it would be simple enough to do by hand provided you don't need the spacing ultra precise.

Print crosshairs onto adhesive paper. Stick on, center dot and drill. Sand off and dimple die.

Dimple dies vary in size & design so you'll be limited to the closest match.

Then, how stainless do you need the stainless to be?
Something with higher resistance to corrosion like 316 will probably need the holes drilling and the dimple made on a press. A lower grade like a 400 series would probably just need a center hole then a chassis punch and nut/bolt for the dimple.

Also, the flange from the dimple will stiffen up the sheet massively. Even more if you could offset the holes rather than have them all in line.
Ie, you might be able to do it all with hand tools using 0.9mm 316 stainless and it would still be stiffer than a plain sheet of 1.5mm.