Months long waiting times for a dentist? I'm not sure if that qualify their public healthcare as great. In a months time your dental issue might actually become acute.
A good rule of thumb is to have a CT scan every year for early detection. I have been doing it for the last 5 years and boy it did save me from lots of pain. Lots of cavities are hiding unseen and with no pain.
Brush your teeth, visit your dentist. Yes some might do an x-ray for hard to see areas. But this is not rocket science
Actually, in some places you have to pay a premium for your insurance/social security if you don't visit the dentist at least twice a year.
These control visits qualify as non-acute, and they greatly reduce the amount of acute dental issues you might have.
Granted, this is another Finnish city, not Helsinki.