I think I will have a harder time trying him to allow the surprise attacks after combat has begun.
I understand the thing about surprise is awareness. How would you determine awareness after combat has begun?
I'm not sure what you mean by this. The rules for when a sneak attack is allowed are actually very precise, and it's not a matter of the GM having to decide if an opponent is aware or not.
By the rules, you can sneak attack if one of these two conditions apply:
1) If your opponent is unable to Dodge or Parry. This can happen in a number of situations, the most common being when he is flat-footed at the start of the first round because he hasn't acted yet. This isn't a matter of surprise; even if two guys are facing off in a duel and are totally aware of each other, the one who loses initiative will still be flat-footed and open to sneak attacks, according to the rules. A lot of people think this is counterintuitive, but its one of the most important strengths of the Thief class, and disallowing it will weaken the Thief quite a bit.
Your opponent will also be unable to Dodge or Parry (and therefore vulnerable to sneak attacks) if he is grappled, blinded etc., but these situations are always noted in the rules.
2) If you are flanking your opponent. Note that this is also not a matter of surprise; if you're flanked you can always be sneaked attack, and it's not possible to for example "direct your attention" towards the Thief to avoid it.
The rules for surprise are distinct from these rules, and are applied alongside them. In short, you get an extra action before the first round if your opponent is unaware of you. Surprise helps when sneak attacking since it gives you the opportunity to perform more sneak attacks because of #1 above, but it doesn't in itself grant sneak attacks.
Hope that helps, and good luck convincing your GM.