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Make it thicker!
For illustration purposes I found two (blank) PCBs of differing thicknesses - one is (tinned) double sided 1.6mm thick and the other a 4 layer board (from an old project) that is 4.0mm thick. Both boards are approximately 300mm wide. Clamping both in the vice, I pulled...
(and what you can't see is that I'm pulling *much* harder on the 4.0mm board!)
And a picture tells a 1000 words...
(I'm sure beam deflection formulae (https://en.wikipedia.org/wiki/Deflection_(engineering)) would yield a far superior scientific approach to deciding how thick a PCB you need, but you get the idea
Essentially, the bending stiffness is proportional to board thickness raised to the square. And it's slightly increased by continuous power planes and copper pours.
For the said board size, a metallic frame might be appropriate.
Vibrations must be expected on a vehicle. At worst case hitting the self resonance frequency of your board...
Google "board stiffener". There are various ways to do this.