Especially businesses that are going well and growing organically and the owner/founder is comfortable and has no need to sell.
How do I broach the subject that can optimize the likelihood that they would realistically entertain the idea of selling their company or more importantly selling to me?
In fact, if someone wasn’t at least willing to talk to you about selling, I would consider that a red flag on the business. I’ve always read in business books, or for the CEO’s I’ve worked for, that you should always have the “for sale” shingle outside your business no matter what.
Also in a way you are flattering them. You think the company they’ve created is so cool you’re willing to spend hundreds of thousands or millions of dollars to buy it. There is something deeply rewarding about hearing that, since all owners have a little bit of doubt no matter how good things seem on the outside.
For actual tactics, I would Google “business broker”, or type that into LinkedIn. Business brokers are like the real estate agents for buying businesses; it’s been the default model for the last couple of decades.
EDIT: even if the business is doing fantastic you can always play the “what if this is a bubble” card. They could lose everything overnight, especially as this trade war heats up, and you could eliminate all of that risk for them.