It sounds like you're just getting really bad RNG rolls unfortunately. While the beaker is rare, I feel like most players find one within the first week, maybe 2.
As theFlu mentioned, a quick peak at the loot.xml will tell you that beakers in general are very rare, ranging from "veryLow" to "medLow" in probability, which translates to a 5-35% chance of looting that item. 35% might not sound that bad, but then you have to take into account that when looting, depending on the container, there are also other items that have an equal or greater chance to be selected, and you have to loot very specific containers in the first place. Your best bet at any loot stage of the game would be in Pop 'n Pills crates as well as T3, T4, or T5 reinforced loot containers. Those all carry the "medLow" probability. They're also found in medical piles, chem stations, and medical air drops, though those are all (except for the air drop) pretty low probabilities.
Tier 2 quests also appear to have a chance of rewarding the player with a beaker, but your base loot stage (if I'm reading the file correctly) must be 3 or 4. The chances are 33% and 42% respectively (but again, there's several other items that can be rewarded besides the beaker.
In answer to your general question of whether or not certain items are locked behind loot stage, I think I've heard that is the case, but I'm not familiar with the code enough to say definitively. If it is true, the beaker is not one of those items.
