I'm sorry you've been through this. Listen to social services' advice. I hear horror stories of them forcing children to see abusive parents in contact centres so what your ex-H did must be appalling for them to advise NC with your child. If he is so abusive surely you could never be happy leaving DC in his care so just forget him and be glad he's out of your lives, and your DC is young enough that they'll have little memory of him and he won't have done too much damage to them. Keep it that way. Do not cling to some idea of DC seeing him because it would make your life easier. It absolutely won't, and will also be so damaging to your DC to have a father like that in their life. My children's father also has no contact at all with them and only would over my dead body.
It is hard to be a lone parent, but you do it because it has to be done. I've been alone with my two since they were babies. No family help. Juggling work and caring for them is very difficult but that's mainly because they both have disabilities and so do I, which makes things much more expensive and exhausting. If none of us did it wouldn't be too difficult as all I'd need to do is work and care for them, not have effectively a third full time job as well consisting of fighting various public bodies to get them support and medical treatment. I don't sleep much. 🤣
Anyway, hopefully that side of my experience is not relevant to you. And with just one child it will be far easier both logistically and financially. One of my biggest struggles is getting sufficient 1:1 time with mine and you won't have that problem.
I recommend getting everything into a routine as much as possible so it requires the minimum input and effort from you. For example, I have a shopping delivery slot that is automatically booked each week for the same time, so have a diary reminder to update the order two days beforehand each week and that is all the effort grocery shopping takes me. 5 sets of uniform once your DC is school age so you only have to wash it at weekends. Batch cooking food once or twice per week means there is a constant rotation of healthy, tasty food but for the other 5 or 6 days there is minimal cooking to do. The more you can do on auto-pilot of routine with minimal brain space and mental effort, the easier it is. Set days for washing, cleaning.
Also find a local babysitter so you can have occassional evenings out with friends. This makes a big difference mentally.
Also, think about the positives: your child won't have to go through the usually damaging additional disruption of step parents or blended families. You can give DC a stable home with no more trauma that isn't dependent on anybody else or can be ripped apart by a relationship breakdown. You will have a very strong bond together. You will not have to deal with negotiating contact with an ex, or missing some of your child's birthdays or Christmases. You can live your life however you like and raise your child how you want to with no interference. You are free now. Look forward to the future! And yes, it will get much easier over the next couple of years as DC gets older and more independent. All the best parts are yet to come. 