Chances of Getting a New Tourist Visa After the 10 Years Ban

Hello, it's been over 10 years that I have waited to go back to the US.I oversayed my tourist visa,for a period of 3 years,during which one my daughter is born...(I did not get married).
I left the country on my own decision(no deportation).
At the airport,I never returned the i-20 form the immigration officer stapled to my passport when I entered the USA (faking to have lost it...) .I thought this could help not having any trace of overstay...
I am now married and in a very stable situation and I would like to visit the US again.
Would I have any chance to get a tourist visa,knowing that the 10 years ban have passed?
Thank you in advance for your answer.
Best regards
Ps: my daughter (12 y old) regularly visits her father in NY

There's a strong chance you'll be denied for having suspected immigrant intent. You should consult an immigration attorney.

Thank you for answering.
Do you think an immigration attorney can help in getting a visa?
Or are you suggesting to check with an attorney just to confirm that I will be denied?

An immigration attorney can review the detailed history of your case and, if necessary, help you with your petition and advise you as to what you might do at the port of entry if the immigration officer seems disinclined to allow you to enter despite your having been issued a visa.

If you apply for and receive a visa, though, the odds are that you'll be able to enter. It's no guarantee, and you should be prepared to document your strong ties to your nation of origin -- property ownership, leases, family ties, jobs, your return ticket, etc. -- just in case questions come up about your intention. It's up to you whether you want to consult an immigration lawyer before petitioning for a visa, after a denial, or even after approval if you want some case-specific advise as to what to do if questions come up at the port of entry.

Thank you very much for your answer.
Do you think that the first step should be to apply for a tourist visa and then speak with an immigration attorney?
Just in case...I have checked if my country of origin is in the list for the waiver program.Unfortunately,it is not.