The mulch could have contained the seeds; I had that happen to me this year. The easiest way to deal with it is to culitvate or rake the mulch - just stir it around - while the weeds are just seedlings. That will take care of most or all of them.

The first year of any "new" garden spot is usually going to have some kind of invasion. Once those seeds sprout & are destroyed (before dropping a new crop of seeds,) there shouldn't be another explosion next year... but there are always weeds to pull. Check often & pull while still small & easy (or mangle as described above.)

A hoe is your friend for seedlings so small.

Yes, a more established garden isn't like that, (unless you planted a bunch of seed-dropping plants.) Don't get discouraged!