I'm a newish stay-at-home mom finding it hard to connect with my spouse, my friends and my "old" life. I have no family support system and none of my friends have offered or shown any interest in helping with my little one. My whole life has turned upside down (not unexpected) but I guess it's my other relationships that have me surprised.
I'm no longer invited to anything friend-wise and the few things I have been invited to were mere hours beforehand with no time to secure a sitter. My husband complains that he hates his job, he doesn't help much with our child — she's very attached to me, which is a sore point — and is irritated that I'm "always tired and angry." I am always tired and usually frustrated that I have no time for myself. He tells me to ask for help and then when I ask, the response is, "OK but [little one] is going to cry the whole time." I don't resent my child, but it's hard to stay positive and upbeat when I feel like only my life has changed.
My husband's answer is for me to hire a nanny or get involved with a mom's group but that doesn't solve anything with my current circle.
Actually, it probably would.
Your "current circle" problem is a specific one likely rooted in your more general problem of being out of balance at home. That's also true of the other specific problems you name: no time for yourself, lonely, always tired and angry, marriage faltering, father not bonding with child — even the husbandly chore-dodging and work-griping.
Your husband's suggestion to hire help is a deceptively significant start to solving it all. Just a few weekly shifts for a part-time caregiver can give you some time to yourself, which can give you some rest, which can give you some energy, which can remind you who you still are with all the roles and requirements stripped away. Hiring help can also get this core self out the door on a date with her husband or dinner with friends or just on a long walk where your soul goes aaaaaaaaaaaa.
A better rested, less angry, more you version of you can say calmly to your husband, when he complains the baby "is going to cry the whole time": "You're right, she will. That means we need to swap roles more, though, not less. We let things get out of whack. It'll take some time and work for both of us to fix this, but soon she'll figure out how brilliant her dad is." Commit to building his confidence with the baby and yours without.
The best way not to slide back into your current imbalance is to make these standing appointments, and keep them. Pick a weekend morning where he's solo parent; a date night; an out-with-friends (or solo) weeknight.
Happier people make more cooperative partners make better parents.
And, employees. Few people think clearly when they're stressed, so easing home tension can ease his work tension.
And just by getting out with your friends more regularly, you can develop a better understanding of their place in life — and develop expectations of them accordingly. If I gather correctly that you're the first with a baby, then I hope you'll see: A baby is so far from their reality that it's no wonder they haven't "offered or shown any interest in helping"! People new to babies (and a few veterans even) tend to see one as a fine reason to run the other way. It's not personal, it's just … alien.
And it's OK to talk about that. Sympathetically, for best results: "I realize you're not in a baby-friendly place." And, if true: "I doubt I'd be myself if I didn't have one." Think of your friends individually, versus as a group, and identify the most flexible. That friend might be open to coming over, holding the baby, enjoying your company while rolling with small-kid disruptions.
A mom group is a fine idea, too, in place of this or (ideally) in addition to. Nothing beats shared experience, laughs and child care.
Please note that all elements of the solution I'm proposing involve more time with others. Somewhere in our societal evolution, a "stay-at-home" parent stopped being communal and became an island of two, parent and child — and that's so counter to what keeps most of us healthy. Parents — whether working for pay or not — are most effective when serving as the leader of a team of people who care for and about their children, and that includes people who care for and about the parents themselves.
So even if you reject this or that suggestion I've made, or if hiring a caregiver is not workable financially, then make sure whatever steps you do take hinge on easing your isolation. "Island" living is wearing all of you down, and it's not how things need to be.