At the beginning of the war, everyone can entrench to level 3 (but some forces are spawned with higher entrenchment levels, eg 8 at Fort Monroe). Level 4 becomes available in late '61, 5 in '62, up to 6 I believe.
Most battles earlier in the war relied on terrain features for field fortifications, as typical battles were between mobile forces. Axes & saws were at least as important as shovels for the very first stages of field fortifications. As an example, log fortifications were thrown up on Culp's Hill in a day's time that allowed a Union brigade to stalemate a Rebel corps - you will not see such bastions built so quickly in CW2. The masterful fieldworks at Spotsylvania and Cold Harbor were likewise thrown up in a matter of days without extensive preparation or planning.
Perhaps a more accurate modeling would be for the spped of entrenchment to accelerate as the war progresses, in addition to the advancement in the attainable level of entrenchment. It might also be beneficial to make the engineer bonus greater