That may be what happens most often but really the matter remains what kind of person you are getting it from. If you don't get an explicit description of strength with or without asking for it you probably shouldn't just assume it's weak.
Some people treat their first time as their virginity and have an idealistic image of how it should be. Some may consider an unexpected low dose for their first time a failure and a big shame.
I don't see it that way and furthermore you risk an unexpected high dose if you don't take it slow. First of all, don't get your hopes up too much, of course it's okay to be excited about such a wondrous thing but expectations can ruin it a little and a sober approach leaves more room for beautiful things to happen that are not foreseen. OK maybe it's hard to ruin the magic of LSD, but if your first time is a mild experience it's like a small taste inviting for more, like dipping comfortably in a pool or sea before going in another time to explore it where you can really swim or go even further and see fish underwater.
Jumping in the deep end can dazzle you in the wrong way even if LSD is forgiving in more cases than mushrooms I guess. It leaves you with getting off on the wrong foot, a relationship with the stuff immediately associated with anxiety. It's possible.
I don't mean to scare you honestly, just a fair piece of advice to be careful taking to much of a batch you don't know anything about.
The headspace is very clear IMO like getting the feeling your whole experience is expanded, taking place in a much bigger space, freedom and clarity... it's easier to look more deeply, at yourself and at what's around you, get a good understanding but also learning to accept things and leave them in peace... taking things for what they are.
It might not all come to you this way immediately and take numerous trips to become more and more clear, and on the way it can take some effort on your part to learn how to deal with things. Apart from visual disturbances, concepts and other things may appear distorted or amplified, sometimes this is hilarous and at other times it can be confusing.
What you expect sounds pretty close but I feel like the 'wonderland' experience is more that of the fairytale-like mushroom trip. Acid is more sensible and rational, but it can still just as well have a magical component. It takes bigger doses to get archetypal though.