From what I've heard, I think your problem may be in assuming that you need the 2 months of training to have a chance.
Yes, if you start attacking people right off, you'll get caught. But if you start off by trying lower-risk options (like burning grain stores, delaying travel, and whatnot), then from what people have said who have tried this method, you have a decent chance of success even at lower levels.
...Perhaps what needs to happen is that the lowest-risk options for most infiltrator actions need to reduce the chance of success further, but also drop the chance of capture down to nearly nothing, as that is what will most quickly end an infiltrator's career. Would you be willing to accept (say) a maximum 1/5 chance of succeeding in burning stuff down, if you knew that there was a maximum 1/100 chance that you would get caught doing so?