Assuming you stayed in the US the entire time after you entered, you meet the Substantial Presence Test for 2019, so you are a resident alien (though you might be a dual-status alien for 2019 (resident only since entry) if you arrived in the middle of the year).
If you are dual-status, you can use Choosing Resident Alien Status to be treated as a resident for the whole year and file as Married Filing Jointly with your wife. So no matter if you are dual-status or resident for the whole year, you guys can file as Married Filing Jointly, and claim your step-daughter as dependent. Assuming you don't have an SSN, you would apply for an ITIN together with your tax return. (Or, if you don't want to apply for an ITIN, you can wait until you get an SSN to file tax returns, applying for an extension to taxes if necessary; or file separately first and then amend it to jointly once you have an SSN.)
Or, you guys can file separately. You would file as Married Filing Separately (which might mean that you don't have to file if you don't have any income), and your wife would file as Married Filing Separately, claiming her daughter. You do not need to apply for an SSN in this case, as your wife can write "NRA" where it asks for your SSN/ITIN. It is almost always more beneficial tax-wise to file as Married Filing Jointly than Married Filing Separately.
As to whether you can file Married Filing Separately and she file Head of Household, claiming her daughter, that is more complicated. She can only file as Head of Household if she is "considered unmarried". Although she is married, she can still be considered unmarried if you guys lived apart for the last 6 months of the year (she didn't) or she is married to a nonresident alien for any part of the year. The latter would be true if you are a dual-status alien for the year (i.e. if you first arrived in the middle of the year).