It would be a pretty complicated process. There were a lot of structural problems within Germany which made reforms difficult:
- Prussia made up 2/3 of Germany, so their state government basically had all the power.
- In Prussia, there was an unequal voting system - rich people (usually the nobility) had more to say than people of medium income, who had more to say than the peasants.
- In the northeast of Prussia (the original Prussian areas), the "Junker"-System was prevalent - big (German) landlords possesed and controlled everything, the peasants (many of Polish origin) basically had few economic possibilities. A remnant of the time when Geman knights conquered the area. A lot of people from the ruling class would have liked the same for all of Germany.
- There was strong sentiment to create a medieval caste society - where people are usually born into a position in society, where wages in professions are determined by common believe of what a person from a certain profession should earn and markets are protected to keep it that way, and so on.
- Minorities (Foreigners, Jews, Polish, Intellectuals, Oppositionals, sometimes Catholics, and so on) were supressed in a lot of ways - difficulties entering a respected profession, ghettoisation, police brutality, unequal treatment of people by authorities often including the judiciary, and so on.
- Whenever a group of mainstream society got into trouble (joblessness, economic decline, or the likes), minorities who happened to be less in trouble at the time or just unpopular were made responsible. So there was a lot of popular pressure against any modernization of society and already a lot of unrest with just the few steps taken.
Basically, everyone who had or was something was under the impression he or she only had it due to such unfair conditions and their own struggle to keep them up. Therefore, it would've been difficult to reform the system peacefully. Especially as that would definitely have had disadvantages for a lot of people who were held up only by the system. Whenever things were tried that were against the interests of the Government (which was also usually part of the upper class) a dictatorship was possible - as happened before. People also were never really interested in long term effects of any reform. One of the reasons why Germany was economically pretty weak, despite a lot of industrial and military muscle.
That's also some of the reasons why Germans contributed so much to US and other population growth.
The slow rate of reforms actually happening may have been the fastest the system could handle.
I suppose only a very intelligent person who wins the position of chancellor with a rather conservative agenda but a lot of reform secretely on his mind could have achieved a rather peaceful transition of Germany into a modern country. It also wouldn't have been a matter of making a decision and pushing it through - rather, it would have been a matter of using and sometimes trying to create or increase popular sentiment to push through one reform after the other - resisting and weakening popular sentiments which are unproductive as much as possible at the same time.
A popular uprising might have been needed to transform Germany into a constitutional Monarchy. An embarassing abuse of power by the Prussian government might have been necessary to transfer their power and representation to the "counties" of Prussia, after which a real reform of the federal system would be possible. A press campaign, supported by most parties, might be needed to get done with the unequal voting system. A lot of propaganda for more competitiveness might be needed to clean up the German "caste" system. A lot of fuss about bad treatment of minorities might be needed to protect minorities better. And so on. Some flexibility to turn counterproductive popular sentiment into sth. useful might also be good - when a campaign against a minority cannot be halted for instance, enforcing melting pot strategies which are helpful for the members of the concerned minority in the long term.
If all this were to happen, loosing WWI might not have had such desastrous consequences for Jews, Roma, Communists, Intellectuals, Homosexuals and so on. Instead, we'd have lived through a few rather "poor" decades and a normal recovery later - similar to France after 1871. With more peaceful interaction with the neighbouring states and better international integration, a policy of not starting unnecessary wars might be the result of WWI - not revanchism.
But I doubt Europe was ready for lasting peace at that time, even with such changes...