Being exposed to Sars-CoV-2 does not necessarily mean you will test positive.
As soon as your immune system detects the virus it will be trying to fight it. As you've been vaccinated your immune system already has memory B & T cells that can recognise the virus and you will be mounting a robust immune response. If you are able to keep on top of the virus quickly enough, you will not test positive.
If your third dose was recent you will also still have active antibodies already produced without having to wait for your B cells to produce them; this is one of the reasons why the boosters are effective at preventing infections and not just against severe symptoms.
Even if you do test positive, that doesn't necessarily mean you are infectious, nor that you will have any symptoms.
If you are young, a healthy weight, fit & active, eat healthily, sleep well, relaxed, thinking positively and not feeling stressed, these will all reduce the chances of an infection developing. You may not be all of these things but if you can just be some of them, every little helps