But it seems that other people here know a increase the speed by using settlers and other cities
Not directly, no.
A single city that is responsible for training all of your units, constructing all of your wonders, and generating all of your research is necessarily going to be "slow" at some aspect of this.
Training a settler offloads some of that work, so that this city can focus more specifically.
But that, and the acquisition of production boosting strategic resources (already mentioned above) is about all the second city can do to help with early wonders.
The one piece I didn't see you mention is the use of the whip - either directly (to finish construction of a wonder) or indirectly (building something else, and applying the overflow to the wonder). Sacrificing population to complete a wonder shaves a couple turns off of the construction time. Trying to leverage overflow is usually going to be slower then just constructing the wonder straight out, but there are cases where overflow production is greater than what you can achieve through more normal means (in which case, you probably aren't going to win the race to an early wonder).
Good point. I once had to build a wonder in a city that had nothing but seafood, floodplains, and one cow tile. That was kind of awkward... I basically had to build one turn's worth of warrior, then whip it, switch to the wonder, let the overflow apply to the wonder for a turn, then build another turn's worth of warrior. I had to stop after a while as my unhappiness level in that city got too high despite my early find of gold and stuff. But it can be done.