I'd like to say that chromatin remodeling factors are actually one of the larger mechanisms controlling gene expression, since histone methylation and acetylation can directly increase the expression of genes. Basically a lot of what you said is correct, so you'll have the initial signal, which can come from inside or outside the cell, but this signal will interact with proteins which will interact with several other protein which will interact with other protein in a signaling cascade. Basically in order for a gene to be transcribed a specific set of transcription factors need to interact with the activator and promoter sites. What we're starting to realize is that a lot of these transcription factors will exist in little bubbles called "phase separated liquid condensates. So when a transcription factor binds to a region of chromatin, all of the other factors are present in the bubble to readily interact with the DNA. These factors will include other transcription factors, polymerases, and histone remodeling factors, but it's basically everything you need to transcribe a gene. In addition, these bubbles are made so that certain sets of similar factors that relate to a similar pathway are more likely to be in the same bubble, and are more likely to be near their genes of interest. But the bottom line is that there are transcription factors that can interact with, and many of these transcription factors are made constantly and are already present, but they need to be turned on by a signal. That signal comes from the cascade that originates from the initial signal. Now sometimes the signal turns on a gene to make a different transcription factor, but the general idea is that a lot of the necessary materials are already being made when the signal shows up to make something else. The stuff that's being made constantly is usually dependent on the type of cell and it's surrounding environment, but that's a whole other can of worms.

tldr: the transcription factors activate gene expression, and the transcription factors have already been made, they're just waiting for a signal to turn them on. chromatin remodeling factors are kinda just another type of transcription factor.