Make sure your tyres are at the correct pressure. Back in the 'last century' recommended pressures were often in the 20's (with perhaps an option to raise them for heavier loads or high speeds) . A few drivers still cling to the old familiar lower pressures as it gives a slightly more comfortable ride - but uses more fuel.
Also compare your pressure gauge with one or two others. Some are not very accurate.
Check nothing is hanging too low underneath. Maybe an under tray is partly unclipped or an aftermarket exhaust/cat is not 'tucked away' as well as the original.
I'm dont think you will have much success improving ground clearance significantly with diffrent tyres or different sized wheels. The combination of wheel and tyre generally need approximately the same rolling circumference so that the cars overall gearing and speedometer accuracy is not affected .Thus a 15" wheel will have tyres higher side walls than a 16" wheel , with overall size roughly equal. It might be possible to gain a bit of ground clearance by fitting a non standard tyre size but any significant gain may e affect the cars gearing and driveability , and would need to be declared to insurers.
If you are due for a tyre change anyway All season tyres sometimes have about 1mm more tyre tread depth than standard (and of course a new tyre with maybe 7mm tread depth gives a slightly higher ride hight than tyres worn down to say 2mm) Its also possible that an 'XL' (extra load" version of a tyre may have slightly stiffer side walls.
If you do wish to explore options for different wheel and tyre sizes the following site includes data on any ride height gain . But i'd be wary of changing specifications.
https://www.willtheyfit.com/No offence intended here. Although some situations are unavoidable (eg grass down the centre of the road' ) you might be able to minimise grounding by upping your hazard perception of the risk.
Cars will often ground when reaching the bottom of a dip, when the weight of the car still pointing down hill when the road rises. This can be worse if you spot the danger a bit too late and add braking to the mix. The front of the car dips even lower under braking. If you can brake and slow earlier you can actually reverse the process by accelerating just prior to crossing the hazard . The car will settle back on its springs raising front ground clearance slightly, which may be enough to avoid grounding. Time this correctly you will not have gained any significant speed when you 'hit' the hazard.
