Hello ! I'm Greek resident and I came in usa with the waiver esta . Now I'm illegally in the US one year . The only solution for me is to get married

Yes as long as you entered the country legally, and you marry a US Citizen, you can adjust status to LPR, even though you have accrued unlawful presence. Be careful not to leave the USA while awaiting adjustment, or you will trip the 3 or 10 year bar. Retain counsel anywhere in the USA to represent you once you marry your fiance.