It is pretty difficult getting the required experience, almost a catch 22 situtaion. However if you are young enough (max 24 I think) you could do an apprenticeship as this is by far the best way to go about becoming an aircraft engineer. As for doing the A licence this is a waste of time if you want to be a B1 (mechancial) engineer. Do a full B1 and your lack of experience will only allow you to use part A of your licence until you have the required experience anyway.
Why do you only want to work on Boeing/Airbus?? There are plenty of others out there.......