Another interpretation could be the first time a person shares an important achievement or news with their mom. For instance, the first time getting accepted into a dream college and sharing that joyous moment with mom. It's about those precious first - time experiences that strengthen the mother - child relationship.
It might also mean the first time a child goes on a long journey with their mom, for example, the first time flying on a plane together. This could be a memorable and bonding experience for both of them. There are many positive and innocent things that could be associated with this phrase.
In a non - inappropriate context, 'First Time with Mom' could refer to the first time a child experiences something special with their mother, like the first time going to a big concert together, or the first time cooking a meal as a team.