Yes, BELIEVE and be baptized. Baptism is a commandment but it is done AFTER we come to faith. If you depend only on works, you will be lost. You come to faith and then you do the works God has called you to do. If you are only depending on your works for salvation, well, you aren’t going to make it very far. The eucharist doesn’t save you either. We take it in remembrance of Him and we do not believe it is the actual blood and body of our dear Lord. It is a spiritual remembrance, not a physical one. Others have explained this so much better than I can.
The Church does not teach salvation of works only.
The Baptism and the Eucharist theology you describe is not scriptural, except that, indeed, when someone is baptized either he has to have made an informed decision about it or if he is not of age or not of sound mind, then he needs a sponsor who decides for him.