Sex life after baby

It’s been about 3 weeks since my husband and I were intimate. I want to, but it’s like we’re out of sync, I’m keen in the mornings but he either has to go to work or likes to sleep in on weekends, the day is filled with caring for our 4 month old and household chores. When he gets home from work, We’re busy with baby until he goes to sleep for the night around 9:30pm and by then I’m exhausted and just want to relax or go to bed. I feel bad because the only time we really have quality alone time is when baby is in bed and I’m shattered from having the baby attached to me for most of the day and sex is the last thing I feel like doing. I don’t know how to get to a place where we’re both in the mood at the same time. I don’t want to feel like we’re just doing it because we should. I love my husband, he’s so supportive and doesn’t pressure me or nag me for sex, but I feel like we’re missing out. Any mums out there been through this and have tips on how you adjusted your sex life after baby?