If i gave birth to a baby in August 2020, and gave up for adoption. Can I still claim the child? The adoption was not finalized until 2021

Probably not - if you gave the child up for adoption at birth (or shortly after), then you would not meet the support requirement or the "lived with you" requirement. It does not make any difference when the adoption became final.

One requirement to claim a dependent is that you must provide more than 50% of their support, which is the cost of basic life necessities such as food, lodging, clothing, medical and dental care, education, transportation, utilities, and so forth.

To claim a child as a dependent, it is also required that "they lived with you for more than half the year (exceptions apply). Even if one of the exceptions applies, you appear to have failed the support requirement.

See Who can I claim as my dependent? for additional information.