(Caveat: This post is aimed at writers who want to make a career of their passion. That isn't everybody's goal, and I don't want to waste your time if you're looking for ways to make writing more enjoyable. There are folks who are better qualified on that subject than I am.)
TL;DR Connections help but aren't a requirement. You can make connections. Agents want a writer they can work with.
In some posts recently, I've seen comments where people talk about "connections." I want to address that for a moment. (I'd say real quick, but I'm a novelist. Almost nothing I write is short.)
First, the idea that you NEED connections to get an agent's attention. Otherwise, unless you're a celebrity already (which means you already HAVE an agent, or if not, you have an agent knocking on your inbox because of that viral video you made), you're NEVER going to get an agent to pick you up. So, say I'm a literary agent, and that I'm like EVERY literary agent out there, following the same business model as all the rest. Only celebrities, or only people who have the right "connections." If you don't have those, I'm not going to bother with you.
Why do I bother with accepting submissions from nobodies? Why deal with dozens, if not hundreds of emails pitching stories that I've already decided don't fit qualifications that don't match what's on my website? I mean, if you have the "connections" I require, then they are going to get you in touch with me, or they'll call me to tell me how cool you are and they'll make that back-room deal through me.
"Well, you want to keep up appearances." For who? Nobodies who don't matter to me? The government? The Illuminati or the Lizard People? All I have to do is put a notice up saying "Not accepting new clients at this time" and close submissions. So, the way agents do business right now is counterproductive to a system that is closed to someone without connections or fame.
That isn't to say connections don't HELP. They do. But therein lies the other myth about connections. "Unless you HAVE connections" basically assumes, by the way it's phrased, that if you don't already have those connections, you're screwed. The thing is, you can MAKE connections. Sometimes it's as simple as talking to someone in a hallway at a convention. Or as simple as messaging a successful author about e-book pricing here on FB and striking up a conversation about something you have in common.
Or, you can do something bold like my friend Ronnie Virdi did. He had the cover of one of his books etched on a beer glass prior to a workshop Kevin J Anderson was going be teaching. Seeing him at the hotel bar, he had his glass sent to Mr. Anderson with his favorite pale ale. That got some peoples' attention, including Jim Butcher.
The point is, you don't have to already BE an industry insider to make connections. Just talk to people, become part of the community, contribute to the community. Make yourself a positive presence.
Most importantly, act like a professional. Agents aren't just looking for someone they like. They're looking for someone they can work with. They're looking for someone they can rely on, because agents don't get paid unless YOU do. And you don't get paid if you don't have a brand worth buying. In the end, yeah a big chunk of it comes down to writing a damn good story. But there is also a big part of it that relies on you being reliable and resilient.