Yea, it starts from the nearest people to the site before it will begin to spread and eventually gets adopted by many people. The challenges of breaking through and being trusted is why new gambling sites need to engage in aggressive advertisements in social media and forums like here by running signature campaign and also have good welcome bonuses to attract new gamblers and then have a working and trusted system to keep them.
Every new site will sometime become old and trusted, just that some few ones try many shady deals with trying to survive their early stage.
You are right those which gambling site can advertise regularly on several platform eg: on the forum, social media, local media as well as print media and overall do search engine optimization along with providing proper support as well as good promotional offer may become trusted to their user and they become successful.
You are very correct, to get reputation the new company needs to partake in aggressive promotion of their brand in every social media handle and in the forums such as this one but not every company that promotes sustains their reputation. Some can spend huge amount of money for promotions but one mistake will their reputation within a short period of time. So it is better to have a formidable team that is very reputable such that after you do your promotion there will be no doubt to continue using your site. A scam company like 1x bit do good promotion but still their reputation is bad, so when good customers are coming others are leaving, it is a problem to the company .