I went on PO, and selected 2 Axew on the teambuilder.
I made one of them have 30 IVs in Atk, and the other one have 31 IVs in Atk. Both had Hardy Nature, and had NO EVs.
I set them both at Level 1, and started to level them up. Here's the results:
Key- Bold: Level, Plain text: Attack Stat
Axew #1: 31 IVs
1 7
2 9
3 11
4 13
5 15
6 17
7 19
8 21
9 23
10 25
11 27
12 29
13 31
14 33
15 35
16 37
17 39
18 41
19 43
20 46
Axew #2: 30 IVs
Axew #1: 30 IVs
1 7
2 9
3 11
4 13
5 15
6 17
7 19
8 21
9 23
10 25
11 27
12 29
13 31
14 33
15 35
16 37
17 39
18 41
19 43
20 45
From this test, I will now conclude that the IVs are like EVs: They accumulate over time. Level 20 is where this one shows up. But, Not all situations will be like this. Some will show at Level 1. For example:
Axew#3: 12 IVs
1 6
While the Axew#1 and #2 have 7 Atk stat, we see here that this one has 6, indicating a lower IV from level one.
In conclusion, IVs can differentiate in a variety of levels, and accumulate over time.
I will also include IV stats for the Axews from Level 30-100.
Axew #1: 31 IVs
30 66
40 87
50 107
60 128
70 148
80 169
90 189
100 233
Axew#2: 30 IVs
30 66
40 86
50 107
60 127
70 147
80 168
90 188
100 232
We can see here that IVs are shown at higher levels, Level 40 being the case.
Hope this helps, and if it doesn't, comment.