Well, the label on the battery saying it's 30Ah (30,000mAh) is almost certainly a lie, given the size of the pack relative to your hand, so I would not really trust the battery or the seller.
If you can return it and get your money back, I'd do that right now.
I'd guess it's probably closer to a tenth of that given the typical construction and contents of packs made by places like that. I don't know what current (Amps, A) it says it can do, but I'd probably move the decimal place one to the left for that, too.
So, assuming they didn't screw up which wires are which, too, then the thick red wire goes to the thick red + wire of your battery case, and the thick black wire goes to the thick black wire - of your battery case.
I can't see which wires are which for your 3-pin charger port on the battery case, but the red wire on the small 2-pin battery connector would go to the positive pin of that port, and the black would go to the negative. To be certain which is which if they are not just two wires, one red, one black, you'll need a multimeter that can be set to 200VDC, and your charger, and a good picture that shows the battery case charger wires and back of that connector, and we can give you testing directions from there.
If you want to use the battery meter on the case, you'll have to splice that in to the thick wires; I'd do that on the ones that are part of the case, rather than the battery, since you can do it without the battery connected, which is safer than modifying any battery wiring.
A quick google for Aoae 30000mAh 48v battery finds several sites selling them. This page
has specs that show their rated capacity can't be correct, because a 30Ah 5p battery would have to be 6Ah per cell, and there are no 18650s with that capacity (and it wouldn't cost $77 if there were).
It is much more likely to be made of cheap low-capacity and low-capability cells or garbage recycled cells, and I doubt it can supply the 20A it says it can, either, much less the 40A peak.
It's possible that their "30Ah" is adding up the total capacity of *all* the cells in series and parallel (which is not how that works), in which case each cell is less than 500mAh. If that's the case, they're *really* bad cells, defective or recycled garbage, etc., and pulling 20A off 5p would be 4A per cell, which would be 4000 / 500 = 8C; I can't imagine cells that bad handling that kind of current very well (will probably get hot).
I also doubt the BMS has a balancing function, so the pack will probably go out of balance fairly quickly, dropping in range until it becomes unusable, or even refusing to charge (if you're lucky; catastrophic failure of one kind or another if you're not).
Product Specifications]
Battery Model: 48v 30000mAh
Battery Type: Li-ion
Nominal Voltage: 48v
Cell Size: 18650
Cell Combination: 5-parallel 13-series
Cell Quantity (parallel*series): 65pcs
Cell Size : 252X95X68mm
Discharge Cutoff Voltage: 36+/- 1V
Rated Discharge Current: 20A
instantaneous Maximum Discharge Current: 40A
Maximum Continuous Discharge Current: 20A
Maximum Continuous Charge Current: 5A
Charge Mode: CC-CV
Standard Charge Current: 2A
Charge Time under Standard Charge Current: 7.5hours
Fast Charge Current: 5A
Charge Time under Fast Charge Current: 3hours
Charge Temperature Range: 0-55°C
Cycle life: 800 times