Get to know your team members as real people. They are not heads, talent, resources, or lines on a spreadsheet. They are real people with concerns, interests, goals, motivations, quirks, strengths and weaknesses.
Try to build rapport with each team member by finding some common interests outside of work and build some type of relationships around it - music, sports, traveling, hobbies, pets, home improvement, etc.
Spend a few minutes of your 1:1 meetings making small talk about these common interests. Your team members, especially remote, will welcome some "chit chat" about something other than work.
Company wide, be sure to celebrate birthdays, anniversaries, birth of children, pet stories, positive customer feedback, etc. For All Hands meetings, see if you can find a volunteer to "tell their story" about a topic they are passionate about. This may also help build relationships.
What do you mean by "improve"? Like mentioned in the book above, I think culture is the examples & acceptable behaviours you set, so do (publicly) what you want others to do.
When managing teams I found out that if I could help people inside the team achieve their personal goals (for example, career growth or even simply their workings hours) in a way that eventually improved overall delivery metrics, I went for it.
When managing teams I found out that if I could help people inside the team achieve their personal goals (for example, career growth or even simply their workings hours) in a way that eventually improved overall delivery metrics, I went for it.