A lot of it wasn't advantages in material technology as we would understand it! Most of it was essentially organizational advantages. "Plans are useless, but planning is invaluable", sort of energy. The Romans could pull off these crazy feats not because they had great tools or anything like that, but basically because they had come prepared. They knew who needed to be told to do what in order to get the job done.

As means of example/comparison... let's say a Germanic tribe wants to cross the river. Well, they'll need to build a bridge or use boats. But Germanic tribes at this time did not have experience in building permanent bridges, so a bridge sturdy enough to take an entire tribe across is already out. That leaves boats. You, High King of the Germanii, ask your eleven subordinate kings - "How many boatmakers do you have?"

... and only three even have an answer ready for you, good or bad, because no one was planning on building boats, and didn't bother to memorize that information in preparation for the raid.

So now you have to wait for each of your subordinates to get back to you, who will all have varying answers with varying precision and specificity - some may include all semi-competent woodworkers as boatmakers, others may only include dedicated specialists they know have prior experience. Some specialists will be missed because their tribal chieftain never thought to mention them, some will be missed because they were simply forgotten about in the mass movement of tens-of-thousands of human beings, some may not have any relevant organization body or fail to mention it to their new leaders. And how many boats DO you need? How many people do you have? How many go across at one time? Safely? Etc.

So you have the query sent 'round, and you get your answers - you have enough boatmakers, however many that is, to make enough boats to ferry the tribe across, eventually. So you give the order to start making boats. Nothing fancy - just some rafts that won't immediately flounder in the current.

... but who gathers the wood? Where does the rope come from? Do we HAVE enough rope? Whose responsibility is it for each boat? Are the tasks divided, with one group sawing the wood, and another binding it together, or united, with each group of boatmakers working on the process, start to finish, at a time? What if regional differences in boatmaking clash? What happens if a raft is botched? Does someone get punished? Who goes across first? Who goes across last? In what order? When do the supplies go? In what proportion? Do different tribes ever need to share rafts? Which ones have feuds with each other? And when the rafts are done, ARE they safe? If one goes down, how do you convince everyone else the rest are safe? Which nonspecialists help the specialists? Are they divided by tribe? What if they refuse? What if manual labor is beneath them, or they have a feud with the specialists? What if they metaphorically trip over each other in the process? How do you sort that labor traffic? Do you even bother? Maybe it's less of a waste of labor to let it be done inefficiently than try to waste time and effort organizing the non-specialists.

And questions like that are endless. I could go on and on, but I think it demonstrates that simply because these tribal coalitions were ad hoc groupings of people who did not always have a clear plan, and certainly not a firm organizational structure, that there are a lot of uncertainties which take time and effort to resolve. Even something as simple as marching from Point A to Point B is complicated by things like this.

Now, let's say that the Roman Legions want to cross a river. They'll need boats or to build a bridge. Building a bridge is something they've trained for, but it is a bit of an endeavor, so let's say they split the difference and make a pontoon bridge, which will need boats and labor.

So you, the Roman general (Legate) gather up each legion's Chief Centurion (Primus Pilus) and Camp Prefect (Praefectus Castrorum), and you posit to them the same basic questions. "How many engineers do we have?" And if they don't know off the top of their head, they have it written down - such specialists are immunes, excused from ordinary labor, and the entire legion has written records in any case; not only are the specialists known, but their location in the camp is also known because each one belongs to a discrete unit whose position in camp is designated, in a camp that is made to a specific and standardized plan. So you bark at your officers, "Go gather them up, we need to figure out what we'll need for a pontoon bridge!" And off they go - and shortly return, because who the relevant people are is clear, and WHERE they are is equally clear.

So the exact number of engineers is rounded up, each of whom has a fairly clear expected level of skill at the task in order to be exempted from ordinary labor (and probably their apprentices, who are not labor exempt and may have varying levels of competence, are accompanying, doubling the number). You ask them and possibly other immune woodworkers, "What do we need to make a bridge here which the whole army can cross in a day's time?"

And that is what your engineers are trained for. They tell you, moving across at a marching pace, from the standard marching order used in camp, departing from your current position, it'll take X number of Y-sized rafts, and they'll need about Z amount of wood. You ask your officers if you have that amount of wood on hand - you do not, and your officers know because the army's storage has pretty firm written records kept too. So you tell the officers to set up labor details - each Roman Century is organized so that the transmission of these orders is passed quickly, and they're organized and trained to divide up for labor like this quickly. And they quickly deforest the surrounding area, drag the relevant wood back to where the engineers need it.

Your engineers are not from a dozen different traditions of woodworking, with barely a common language between them - they all have been trained as immunes from other military engineers - they are all working to roughly the same ideas and same plan. If someone fucks up, everyone knows who gets punished, and even HOW they get punished. Everything is neatly organized. They know what kind of rafts need to be made, what modifications need to be made to turn it into a pontoon, what they need for it, and they have the entire rest of the army (more or less) ready to assist them with manual labor when ordered to, because the entire rest of the army is trained and prepared for just that.

As soon as the bridge is built, the troops can start crossing - each one organized by their pre-existing and (fairly) evenly divided units, as commanded by a clear hierarchy of officers which can transmit instructions. They know the order they leave the camp in every day, and because no one is stupid enough to quarrel with their Legate, who holds unquestionable power of life and death over all of them. These legionaries are not "Come and go as you please", like a confederation of tribes, they're all men who've signed up for distinct terms of service, with the expectation (and enforcement) of rigid discipline. Their only alternative to obedience is desertion - and desertion is punishable by crucifixion.

No one is going to say "12th Legion are thieves, I won't bring the supplies across if they're over the bridgehead before us!" the way tribes might quarrel. Even if the individual legions hate each other, the notion of being flogged, and knowing that Roman discipline means you will be flogged, not just 'might' be for attempting to dispute time-sensitive orders, has a way of quieting tongues. Viciousness of the punishment aside, what matters is that it is undesired and that it is reliably applied - that is what quiets the troops to obedience in the moment.

So everyone knows what they have to do, what they need to do it, how to do it, when to do it, in what order to do it, in what way they should do it, and they will not be quarreling or trying to negotiate in what way they will do it in.

Organization makes the impossible possible more than any material technology.