I'd definitely wait to bring up the topic until you've been there a while, are fully ramped up and performing well at the job. I'd raise an eyebrow if I had a new hire asking about working from home before they even knew where all the conference rooms were located in the building!
Also find out what the company policy is on working from home. Sometimes, they only allow people with specific job functions to WFH, or people who live a minimum distance away from the office. Or each WFH day has to be pre-approved, etc.
My current workplace has a "you can WFH one day a week, IF you can fulfill all the job functions you have to do that day from home". Sounds easier than it is, but we actually have a fair amount of meetings you need to be physically present for rather than dialed in. I almost never WFH, I feel like I don't get as much done, but I do it occasionally if I've got a cold and don't want to spread my germs, have twisted my ankle/knee and need to stay off my feet, or am expecting a furniture delivery. I value face-to-face interaction, whiteboarding sessions, and the synergy and ideas that spring from impromptu water cooler discussions, so it's important for me to be on-site.
Congrats on the new job!