Can I estimate tyre pressures on a road bike?
No, not really. It is difficult to get an accurate idea of tyre pressure by pressing it.

Especially for thin, high pressure road bike tyres - they should feel pretty hard. Even if they do feel hard, the pressure may be much lower than it should be.

Best option is to get a good pump, with a built in pressure gauge. Many mini pumps will take a lot of effort to get the pressure high enough, a 'track pump' would be a lot easier.

Tyres do lose air over time - especially thin, high pressure tyres - so it is a good idea to check them regularly, and inflate as required.