G.♣.
When I was a SAHM I definitely missed working, the social interaction, being with other adults, etc. When your child is very little (like 2 or younger), it's especially hard because they are not old enough to really do anything in a group.
When my oldest was about 18 or 21 months, that' s when we started doing things. We joined a playgroup that met once a week. We signed up for 2 classes (park district & YMCA) that were parent/child classes. These things help! I had a chance to interact with other parents (mostly moms), and it got us out of the house a little.
You might also consider a part-time job. You likely wouldn't make much money, but you would work less hours. Or do some volunteer work - at your church or a neighborhood school. What are you passionate about?
This is a very short season in your child's life. It's not always easy to be a SAHM. It can be very isolating. But it won't be long before you can take a class together. It won't be too much longer before your child can go to preschool a couple of mornings a week.
It's so unfortunate that it feels like your only options are to be a SAHM or to work Full Time. Try to think outside the box a little bit. What else could you do that you would enjoy?