I am from Ukraine.When crossing the border, I did not get a stamp in my passport – do I have to get a certificate of the date of crossing the border from the Border Guard before going to get PESEL?

If your entry into Poland was not registered by the Border Guard during border control, you should go to any municipal authority and apply for a PESEL number within 30 days of your entry. By submitting this application you will also be able to apply for your residence to be registered.