[RPG] cast a no-concentration spell while concentrating on another

A spell ends when you lose concentration:

Some spells require you to maintain concentration in order to keep their magic active. If you lose concentration, such a spell ends. Phb 203, emphasis mine.

So if you lose concentration the spell ends, no conditional time given. And we can also see what breaks concentration on the same page:

You lose concentration on a spell if you cast another spell that requires concentration. You can’t concentrate on two spells at once. Ibidem, emphasis mine.

My interpretation of this is that both spell effects can't be active at the same time, thus the enemies won't be restrained.

No. Casting a concentration spell immediately breaks any existing concentration.

One of the rules clarifications in Xanathar's Guide to Everything (pg. 5) addresses this issue directly:

As soon as you start casting a spell or using a special ability that requires concentration, your concentration on another effect ends instantly.