I don't think Sun Quan doubted for a moment since he came to power that his goal was to unite China. He just didn't have a proper excuse, and so he had to resort to being opportunistic in his expansions. Liu Bei could claim his imperial heritage, which gave him license to conquer land (in the name of the Han). Cao Cao was operating under the "unite the Han empire" banner for a long time too, and though he's not a Liu, having the emperor under his protection justified his actions. And the Suns? They had neither pedigree nor power to rely on, and like Six_and_Up said, if they had revealed their ambition too early, a Yuan Shu-like disaster would ensue.
Sun Quan was very clever in letting his advisors speak his mind for him. Look at the three men he employed as chief advisor before he declared himself emperor:
Advisor 1: Zhou Yu. Biggest expansionist in Wu. His Ba-Shu plan was aimed to take over all of China. The end of his speech petitioning Sun Quan to sanction Operation Ba-Shu was "And then, we can have designs on the North." Sun Quan approved of the action. If Sun Quan was content to just protect what he had, there was no reason to risk this campaign.
Advisor 2: Lu Su. He got Sun Quan's trust after presenting the Wu version of the Longzhong plan, which said "...Han cannot be revived, and Cao Cao's power cannot be completely eliminated. My advice to you is to take the Southlands to be as one leg in a tripod.... This is the enterprise of the High Emperor (Liu Bang)." Thereupon Sun Quan bestowed lavish gifts on him and his family (though he had to say something about how he should be supporting the Han instead--time was too early to show his cards). After that, every time Lu Su mentioned something about Sun Quan becoming emperor, Sun Quan would show that he was pleased. Would he have treated Lu Su that way if Lu Su's ambitions did not match his own?
Advisor 3: Lu Meng. The taking of Jingzhou is a clear indication of Sun Quan's ambition. If hanging out being lord of the Southlands is enough for Sun Quan, why bother risking Shu's wrath by taking Jingzhou? Having secured Jing, Wu could then concentrate on attacking Wei. Note that after talking to Lu Meng about taking out Guan Yu, Sun Quan said, "By the way, what about Xuzhou?" (SGZ-Lu Meng's bio) If this isn't an indication of his aspiration to take over China, nothing is
Also don't forget Sun Quan's moving the capital city to Moling/Jianye. The geographical location of Jianye is a challenge to the north
There's also the many northern expeditions, as Six_and_Up mentioned.
All in all, I think the case can be made for Sun Quan's having had designs on the empire since the very beginning. What's stopping him from announcing it to all the world (before AD 229) were two things: the lack of a legitimate excuse, and (though I haven't mentioned this yet), the need to achieve security within the Wu lands (from the Shanyue).