Not married and home is 'pre-relationship' and in your sole name? To my knowledge he has no rights and you can kick him to the kerb.
As far as what you need to do, not in any particular order...
If you have joint banking or assets you need to separate all finances asap and close or get your name off any joint accounts. Redirect any direct debit payments to your 'new' account.
You need to take all your important papers (property deeds, investment papers, tax records, etc) and your joint child's birth certificate, passport, and school & medical records and get them out of the house. Take them to a trusted friend or relative, a bank lockbox, or a secure locked cubby or drawer at work. Same for any sentimental items or items of value.
Change all online passwords even if you think he doesn't know yours.
In essence, you need to 'sanitize' your home of any and all items he could use to either cause you problems or grief with or destroy.
I'd also advise seeing a solicitor, even though you aren't married, to be sure he has no rights to anything AND to educate yourself regarding child maintenance and child access.
Speak to the solicitor also about what to do if he refuses to leave. If they say call the police then make sure your local police will actually do anything to get him out. Be prepared to show them the deeds or other records to prove the house is solely yours.
Sort out dependable childcare for yourself. You most likely won't be able to depend on him.
Do all the above before you give him his marching papers. I wouldn't give him 28 days, I'd just give him until I had all my ducks in a row then I'd tell him to leave and leave now. First off why should you do him any favours? Secondly, it's surprising how many 'nice' men turn nasty when they are dumped, especially when it means the loss of a comfy nest. That's why you don't want him hanging around 'serving out his notice'.
Once he's gone call an emergency locksmith (price first and set money aside) to change the locks or lock barrels. It's not cheap, but the peace of mind is well worth it. Don't trust that he simply returns the keys, you don't know if he's had duplicates made at some time or another. This is especially important if you end up giving him time to find a place to live.