We became cat parents and started fostering cats all in one go, as the stray cats in our college neighborhood would move in when pregnant. Or sometimes leaves us tiny kitten presents in the front yard. We had no clue what we were doing and we rarely were able to have "proper" cat introductions. We worked hard to make sure everyone got along and spent hours a day playing with the different age groups both separately and together. The more we played and spent time together they more they all eventually got along. Sure some of them hated each other at first and some were instant best friends, but as a group it took work.
The next kitten season we had read and prepared as much as we could and had made a separate space for kitten litters. We again had a few litters of kittens and this time kept them separate in the laundry room. We made sure to come in often and spend time playing with the kittens. They all became friendly with us and with each other so we decided after a month it was time to open the door. And off went the kittens to hide. From here we saw that what we thought was friendliness was really less fear, and as soon as they had more space they started running again. The new space and the cats scared them, and now they had better places to hide.
We continued to try separating the cats until they were friendly. We tried leaving in the back room for longer to make sure they liked us. But every time we found the real way to get them happy and comfortable was to constantly interact with them once out in the real environment, and I realized why I didn't like the idea of isolating until friendly.
Cats are friends and family members, they require constant love and attention. Just like with a kid you try your best to make sure their first interaction is good but the real work comes every day. When we separate the cats until we think they're ready we're assuming they will become friendly, rather than seeing their friendliness as directly related to how much love and attention we give them.
When you do bring a new cat into a house it is important to separate for a short period for health reasons and to allow the new cat to have a comfortable area where they can get used to the scents and sounds. If you are concerned about a possible illness then a 2-week quarantine is usually a safe bet. If you are antsy like us then reevaluate them after a week. Just make sure to be paying attention to all of your pets during this time.