Generally speaking, if a tester waits until code has finished being written, they are not going to be able to get the product to their own high level of quality. Time is against you, and developers will eventually start menacing you with nerf rifles when you darken their doorways. The key is instead to smash the bugs before they are coded into existence. This is achieved by becoming passionately involved in the design and spec phase of the product.
There are several non-exclusive ways to do this, the easiest is by testing the spec, and let both the designer and the PM know that you will be doing this. As nothing (hopefully) has been committed to code yet, the changing of a document or picture should be relatively easy enough to convince them to do. The other way is to become ingrained in the designer and/or PM’s process. Test the designs, and check in on their progress on a regular basis. This should last thoughout the product cycle, gradually ramping down to ship as you instead spend more time arguing with the developer.

Unfortunately this means that testers never really get a break. PMs tend to relax close to shipping, devs tend to relax during the planning phase, but test needs to be actively involved the entire time. This involves turning all the bullet points in the spec into questions. Look for consistency, look for bad user experiences, and look for the ugliness before people get too used to it.

The other down side to this approach is that this means both PM and Design will now also start menacing you with nerf guns when you darken their doorway. However the solution to that is obvious: Buy more and bigger nerf guns.