Kinda possible. You can buy coins on some websites focused only on it (like buycoinnow.com or something similar) and then hold them till the time will be right. But in the end, you will have to register on exchange after all.
Would that not be too cumbersome to do, having to open different website because I want to trade some particular coin, Imagine I want to trade about 10 coins, which means I must have an account on each of them, and when it comes to trading, one has to consider the time of executing a trade, before you get to toggle between all the website and login in, time would have gone for you to take execute some order.
I think the best would really still be an exchange, and come to think of it, why would someone not even want to use an exchange to trade since they have the database of most coins in their platform, which will make it very easy for such trader to quickly pick any coin of his choice. What needs to be done is just to ensure that the exchange is a reliable one and that which has a very low trading fee like that of Binance.