I just bought my first set of tires. They were of the folding type. Even after unfolding and leaving them overnight they still had kinks in the bead. It is a bit unsightly but that isn't the issue. Do the kinks affect the way they should be installed?
This is completely normal for folding tires. They will settle into round shape when they are mounted and inflated for a while.
When installing the tires with kinks, they do slip away from rims more often than perfectly round tires. One way to avoid it is to keep the part that is already on the rim tight. There's no need to align the kinks to something, or anything like that.
I got an unused 20" folding tyre that had sat in someone's bag for 10 years. It was seriously zig-zagged when unfolded, but once on the bike it was perfect.
Later I suffered a puncture, and on changing the tube I noted the tyre still wanted to zigzag, but its completely unnoticeable on the rim.
For peace of mind, you might want to lubricate the rim with water when first fitting, and then half-inflate the tube, and give the whole tyre a good visual inspection before fully inflating.
You can also use your thumbs every inch or two around the outside, to push the tyre's sidewall sideways. Any oddness, stop and evaluate. Note that a "pop" is probably just be the bead seating, compared to a herniation where the tyre is bulging out.
Leave the wheel fully inflated overnight before riding the first time, and check it again before your ride.