You'll need to be typed and generally you'll need experience on type. It's not that the companies have such high minimum requirements; it's the fact that there are many very experienced and qualified guys out there who are also keen on positions available.
Without a shadow of doubt; if you're not jet qualified and you're an expat, there is no obvious way to seek employment with a jet operator. The same can not however be said of some of the low-cost operators in Europe. Get a job there, get the experience and then think about the sandpit.
Good luck & best wishes.