Most DMs use the chart from DMG p135 to determine at what point a character should have a given rarity of item. However, I believe that this is just an estimate of when they would be expected to have actually procured one based on odds. Looking at DMG p133 (emphasis mine) you will see the following expectation of hoard payouts over a typical campaign and includes all types of magical items combat, consumable or otherwise:
- CR 0-4 7 rolls
- CR 5-10 18 rolls
- CR 11-16 12 rolls
- CR 17+ 8 rolls
Starting at Table G on the hoard generation charts starting at p137 it is possible to get a “Rare” item. Obviously the odds are against you but in any of those 7 low level hoards it is a possibility. Further “Very Rare” consumables are possible on Table D which starts being found with CR 5-10 hoards and Table I has “Legendary” items and is starting to be a possibility by CR 11 hoards. Keep in mind that a typical challenging encounter is about the same or a bit higher than the party’s level.
I won’t go into all the extrapolations or odds, but maybe someone with more time and a math degree can generate your odds of getting these things at given levels. Or use the chart on DMG p135 as the ballpark.
I actually used these guidelines when we rolled up level 15 characters and I simply rolled potential hoards, they ended up with much more magic items than the chart on p38 starts you at by a large margin. Even with items they would have had to sell or donate they were still sitting pretty.