To qualify for EI you have to have worked at least 600 hours in the 52 weeks before your leave started. So if you're working full time, you should qualify by the time you're due.
You shouod absolutely take the job and keep quiet as long as possible (or until you need any special accomodations). I'm not sure where you are but in my area, as long as you have 600 insurable hours worked by the time you take a leave, you will be entitled to EI.
Take the job, keep quiet. Do not tell anybody at all. Especially while you're on probation because even though they can't fire you for being pregnant while you're on probation they can fire you for any other reason and they can make something up like not being a good fit. You don't have to tell them until you're in well into second or in third trimester I believe. Check their policies, they might have a specific time frame that you have to get everything sorted by, for example at my work my leave date had to be given and approved at least one month before it was supposed to start. And you will qualify so long as you have 600 hours of working in the 52 weeks before your leave starts. As for top up from the company, you may or may not be eligible for that depending on what their policy is if they have top up
I’d definitely keep it to yourself until second trimester and/or your probation is up. Usually 3 months. As for EI you need a certain amount of hours worked between leaves to qualify the second time around. Not sure what that # is I’m sure someone else who comments will know Best of luck to you! 🥰