For the 1st year of life, breastmilk/formula is the PRIMARY source of nutrition for a baby- NOT solids, not water, not juice. This is per our Pediatrician.
ALSO, breastmilk/formula should be given BEFORE solids...not after, or the baby will be too full afterward to nurse, and usually giving solids 'first' is done to WEAN a baby off of breast. I imagine this is not something you want to do yet... and being that he is so young.
You can continue to pump and bank bottles on the side to give to the babysitter. Then, nurse on demand once he is home and once you are home.
Now, if he 'never seems full..." it is either: (1) he is going through a 'growth spurt' and thus, his intake needs are increasing to keep up with his growth. This is normal and natural...you must STILL nurse on demand through these spurts. (2) He is 'not' getting enough intake... which would be indicated by his constant hunger, and he would not be gaining adequate weight/growth at his well-baby check ups. (3) your milk output is not keeping pace with him or is not enough (4) he is not latching on properly or efficiently...THUS even if he IS at the breast, he is not getting enough intake (5) He is not staying at the breast long enough to get enough intake (6) He is "cluster-feeding" which is what nursing babies do at times... and it means they even nurse EVERY hour. This is completely normal. It occurs 24/7. Thus, you still need to nurse on demand. (7) he is constantly 'hungry' because if not fed 'on demand' and only by a 'schedule'...then his feeding needs are not being met, for proper intake & growth.
Do not rely on the 'solids' to make up for his 'hunger.' Nursing should be his primary intake source. You NEED to also tell your babysitter/daycare provider that he NEEDS to be fed on demand- NOT ON A SCHEDULE...and I'm talking about his bottle/breastmilk, not solids. Solids at this stage is merely for getting 'acquainted' with 'food' not as a main source of nutrition and serving size is only in terms of tablespoons or teaspoons.
Always have a "plan B." And if you need to give him formula... don't feel bad about it or insulted. You do what you need to do, and per your situation.
If your baby will not take formula... ask your Pediatrician for advice. Your baby cannot go all day without breastmilk/formula... or they can get dehydrated. Not to mention not get nutrients or proper caloric intake. Very important to keep in mind.
Some babies, will not take anything- breastmilk via bottle or formula ALL day while at a sitter. But... this is not real good. Then once the baby gets home, all they do is nurse ALL NIGHT to make up for not getting anything all day. I don't know if your Pediatrician will think this is "good" for a baby or not... but I know some babies are this way and supposedly do this.
I know it's not easy.... but ask your Pediatrician for other types of formulas he/she can suggest. I used the Kirkland one from Costco myself. My son had no problems with it. And think of a "Plan B" just in case.
All the best, and I hope it works out, take care,