Some banks will issue an approval in principle (AIP) with a condition that they will not proceed to loan offer until probation is completed. This way, you can make offers on properties armed with the AIP (which some estate agents will insist on seeing before they will even accept a bid).
You could get the ball rolling, but if your probation will not be completed until July, you can't really make an offer until June. With this in mind, it would probably be best to get your AIP no earlier than May, as it will only last for up to 6 months.
A key consideration for some lenders is whether your employments are both continuous, i.e. no significant gap between employments.
I completely agree with Brendan's point - a broker could advise you on where you stand, and what changes (if any) you could make to give yourself the best chances of approval with multiple lenders.
Best Regards,
Dave Curry, Irish Mortgage Corporation