If becoming a sniper in the military is what you want then yes, it is by invitation only, however there are ways to increase one's chances in receiving such an invitation. Of course being an expert sharp shooter is quite obvious, but it is also a good idea to be on good terms with your commanding officer, for he would be the one to recommend you.
On top of that you can only be recommended if a spot opens up. If you are lucky enough you will be sent to "sniper school" where you will be taught the basics to the most advance rules and techniques of sniping and spotting. And even this you can "fail" and can be sent back to your original unit... however if you pass... I assume you get the idea
--off-topic---
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