Yes, I do train to enter with very early timing, and I also don't necessarily think of it as offensive or aggresive. But then I'm not big on defensive either. I think aikido kind of steps out of that strict realm of offensive / defensive.
I try to think in terms of sen no sen, sen sen no sen, go no sen instead. But then, not being a native speaker of japanese (or much of a non-native speaker either), I'm not sure how correct my understanding of those terms is. I guess I'm muddling through like most everyone else I know.
I do know that one of my instructors feels that the shite/uke training as practised in the yoshinkan helps to build the focus required to enhance the early timing you speak of. (please bruce, don't take it personally that I'm going to speak from my perspective...the yoshinkan method is not any better than anyone else's, I'm just talking about one perspective on one issue, from my own experience)
When we start a technique, we typically start from about 6 ft apart, perform rei (standing bow)and then go into kamae (basic stance) together. The idea is to focus on your partner so that you both move at the same time, building the ability to sense your partner's intentions. That focus should remain throughout the technique. Then shite moves to the appropriate distance for the technique (shite always sets the distance), and leads for the attack (for front strike, the lead would be to raise the front hand if in aihamni). By leading for the attack, shite gets to feel and observe uke's preparation, initiation, and their actual attack. I believe that over time, this type of formalized training builds the intuition needed to fully utilize "early timing". Of course, YMMV.