No. Excepting some special circumstances that don't apply here like official military travel, a passport is required by the US. Brazil similarly requires a passport. Any airline will simply deny boarding if you show up with only a birth certificate.
For instance, if you go to Timatic and tell it that a US citizen wants to go to Brazil with only a birth certificate, it will say:
No, The travel documents held are not sufficient for the traveler's journey, or they may need additional documents as follows:
Brazil - Destination Passport
You should also review the US State Department's Level 4: Do Not Travel advisory for Brazil. If you do not trust the US State Department, consider also the UK's advice against ‘all but essential’ international travel.
There are also non-COVID health matters to attend to in Brazil depending on where you are traveling, including yellow fever and malaria risk areas, so if your travel is imminent, you'll need to address that immediately.