There are two answers to the question, depending on what you mean by "mandatory military service time".

If you mean to ask whether all Athenian citizens in the Classical period were liable to military service, the answer is yes. When a male Athenian citizen turned 18, they would be enrolled in their deme registry. All the men on this registry could be called up to serve in the army until they turned 60. Since Athens had no professional military, men were called to arms when arms were needed; when war broke out, the taxiarch of each of the ten tribes (administrative regions) would be required to turn out a certain number of men for specific campaigns. If the levy was to march out in full force, every adult male citizen would be drafted.

There is some controversy over how the system of selection worked, since our sources suggest there were 2 different systems. The first, conscription ek katalogou ("from the list"), suggests that the taxiarch hand-picked men from the deme registries to meet his quota, probably giving preference to the physically fit or politically reliable, or those he wanted to have a share in the glory or the spoils. The second was conscription by age group. While those aged 18-59 were all liable to serve, Athenian field armies rarely contained men under 20 or over 45 years old; in order to filter out the young and the old, it had to be possible to group them by age. The most likely process (also known at Sparta) was to keep separate lists of men who had come of age in a certain year, and only call up the years you wanted. The size of the army could be determined by how many years you called up without compromising the number of young, physically fit men in the ranks (so, for a small army you might call up only those aged 20-25, but for a large army those aged 20-40, and so on). Traditionally, scholars have argued that conscription by age group replaced conscription "from the list" in the 4th century BC, but more recently it's been argued that the age groups must have existed before that time, and conscription "from the lists" does not denote some radically different system.

Failing to appear at the mustering point when you were called up to fight was a crime known as astrateia, draft evasion. Those found guilty of astrateia lost certain citizen rights: they were banned from the public square and from receiving any public honours in future. It is possible that they were stripped of their citizen rights entirely, a punishment known as atimia (literally "dishonour"). But people were usually only persecuted if they were already public figures, and rarely convicted.

If, instead, you want to know whether there was a fixed period in a male Athenian citizen's life when he was in permanent military service (like modern conscription), the answer is probably not, except during a brief period of about 335-322 BC.

In that period, between the defeat of Athens at Chaironeia in 338 BC and their defeat in the Lamian War of 322 BC, we have solid evidence (both literary and in the form of a huge body of inscriptions) that Athens subjected all male citizens who turned 18 to a mandatory two-year programme of military training and service. The first year was spent training with weapons of all kinds, including catapults. The second year was spent in the watch, garrisoning the extensive network of border forts and guarding the walls of the city. At the end of this two-year period, each recruit was issued a shield and spear by the state. They would then be eligible for military service until age 60 as before, but now as a trained reservist rather than an untrained militia levy.

The tricky question is whether this system existed before 335 BC. Scholars have debated this for decades, and a lot depends on how you want to interpret the evidence. On the one hand, we have references to an organisation with the same name as the later mandatory training programme existing in the 370s BC, and a reference to the watch as early as the late 5th century BC. Clearly the later programme didn't come out of nowhere; it probably built on an already existing system of military training for young citizens. But we also have explicit evidence from Xenophon that, as late as 355 BC, recruits in this programme weren't being paid for their service. Now, most Athenian households wouldn't have been able to just miss out on the labour and income provided by a young man for two years; Xenophon points out that these recruits aren't doing their training properly because they aren't getting paid, so they can't afford to spend as much time on it as they should. Most likely, the earlier programme was voluntary, and only the rich could take part. This means that, at best, a small minority of Athenian citizens were actually getting this training.

It wasn't until the reforms of 335/4 BC that the programme was made mandatory, almost certainly in exchange for a daily wage so that all citizens could participate without suffering a crippling blow to their household income. This would also explain why we have zero inscriptions listing recruits to the programme before 335 BC, and a huge body of them for the ensuing decade (after which they completely disappear again). The programme had changed; participation rates had exploded; and suddenly it was a matter of civic pride, not just an elite fancy, to train yourself for war.