Without going to the extent and design of the atonement-we can easily say yes. For God desires all men to be saved-fro He is impartial with regards to men-whether Jews or Greek, slave or free, men or women. Old or the young.
However to say that we must baptized our babies because God desires them to be saved-is to misunderstand the biblical term-covenant and the use baptism in the New Testament age.
In the new covenant – baptism is almost always related to salvation-not just merely a intermediate status between the saved and the lost.
Our relationship to our unbelieving children and spouses is holy to the Lord. We need not be ahame of their status.
Our children and spouses can change their status-in any age- by trusting the Lord Jesus for their salvation. Of course, without coercion or undue influence from other adults. Then baptism can be applied to them.
The covenants in the Scriptures are not always of the same characteristic or nature. Some are unilateral-others bilateral. Some conditional-others unconditional. This reflects the covenants existing in the ancient world as well as the contracts in the modern. They are either called royal grant, suzerain treaty and partnership covenants.
To apply a symbol of salvation to children-and say they are in the covenant but sre still not yet saved-is to confuse them and create of illusion of semi-saved status. It could be deadly to their eternal welfare.