I'm 5'4", 125 pounds, 50, average looking.
You're making too much of an issue about your height. It's obvious you're very hung-up about it. Maybe that comes through in your profile or messages, probably does in person at some point. I've had more dates/relationships with women of all heights, including much taller--up to 5'10" in terms of relationships. It's easy to blame things like height or weight when you're looking for explanations about not getting dates, but it's mostly wrong.
Your practical problem is trying to rely on/are focused on women initiating things. Women don't initiate as much as men do. This has little to do with your height. Contact the women you're interested in. Take the initiative. This is just the reality for MF relationships and you. Maybe there's a generational issue given how much older I am than you, but taking the lead empowers you to get what you want.
But yes, if you're taking about Tinder or hookups, casual connections, yes, physical traits are going to matter far more because the emphasis is far more physically-based and being the magic "6-footer" is a bonus. That's life.
A height preference is just that; it is rarely a requirement. Maybe for younger women they are more concerned about it than women in my age range, but my height hasn't been as significant an issue for me online one would expect. I contact women of all heights and am contacted likewise, including often by and to women who state a height range, like on Match, that excludes me.
On lying: It would be a help--initially--to claim to be taller than I am, as some women friends (one is a dating advisor) have suggested I do, given that so many other guys lie and so many women assume men are shorter than they claim to be. In the long run, it's counterproductive to deceive, I believe in honesty, the long-term, and have too much self-respect to lie and misrepresent myself even if it got me more dates and relationships. You are who and what you are; if someone won't accept you as you are, you shouldn't be interested in them.