You could be dilated to a certain number for a very long time, weeks/months etc. 34 weeks is very early. Your Dr should be monitoring you at this point especially if you are having regular contractions
At 34 weeks, it's a bit early to go into labor- is your doctor monitoring you for pre-term labor?
As far as how long it takes to get to 4cm- that varies from women to woman and pregnancy to pregnancy. You could walk around for weeks at 3 or 4- or it could be an hour later and you could be at a 8 ready for delivery.
Make sure to watch for signs of preterm labor- and call your doctor right away if you have them. From the March of Dimes, these are the signs to watch for-
Change in your vaginal discharge (watery, mucus or bloody) or more vaginal discharge than usual
Pressure in your pelvis or lower belly, like your baby is pushing down
Constant low, dull backache
Belly cramps with or without diarrhea
Regular or frequent contractions that make your belly tighten like a fist. The contractions may or may not be painful.
Your water breaks