The place to look would be the Prussian reform movement of the late Napoleonic wars. This is one of the few armies in history to manage anything close to what you are asking for. What this suggests is that you have three primary problems in your setting:
Economics
Why did no one in northern Europe field Phalanxes? Or why was Rome able to adopt the maniple? For these two questions, the answer is economics. These tactical developments required time to train in. This time could not be spent farming, so required agricultural surplices over substance farming that northern Europe could not provide. So you will need to answer the question of where the food and equipment comes from, for a significant proportion of your population to spend there entire lives learning, training and preparing for war, in addition to spending there entire professional lives as soldiers. This was a big constraint in armys up until the renaissance. Rome is one of the few known large states to have a professional army prior to the renaissance. Your Phylanx using invading empire can afford to have its troops at home in the key periods of spring and autumn to farm. Only coming out to campaign in the summer when the crops are growing.
Note that going from Phylanx level to the level of initiative you are talking about is something that will take decades due to the need to first educate enough people to do the training, and then train all of your soldiers from what is effectively primary level education.
Culture
The next problem is culture. Initiative in an organization interacts directly with the culture of authority and rewards. Do people expect there leaders to consult them and listen to their ideas, or do they expect to by punished for speaking out of place? You need a state where the individuals involved feel engaged in the goal of the campaign. Since your setting is an invasion, patriotism should help here. However, they can't be motivated purely by patriotism, as this would not explain how the army would have fostered initiative prior to the invasion, as this is not something that is easy to introduce. As for rewards, you need a society with a minimal level of meritocracy so that the people given these lower ranked positions actually are competent enough to run a squad and want to take risks so they can advance. Finally you need enough education that you have a large enough pool of competent people to command such positions. Most classical cultures didn't educate enough people to provide such a pool.
Weapons
In order for initiative to be useful, you need a way to translate that initiative into damage. This means that you smallest unit of combat must be capable of performing enough damage to overcome an opponent groups defense. This means something ranged like a bow or gun. Its only really in the late 19th into 20th century that guns become accurate enough and have high enough rates of fire for a group split into squads to perform enough morale damage to break a groups charge.