I would like to suggest the following to you:
Team-Building Activities
Initially, you can start some team-building activities, such as games on the last Saturday of the month, or any day when all the field executives and staff are available in the office. The program could last about 1.5 to 2 hours, with a snack party at the end, so it does not interfere with daily work.
Celebrate Birthdays
Celebrate the monthly or quarterly birthdays of the staff. Order cake and snacks and celebrate birthdays along with the games.
Lunch Meetings
As you mentioned, the staff faces many challenges. Initiate lunch meetings with them, department-wise or on a one-to-one basis, to talk to them and encourage or mentor them. Since you are new, it is important to establish a rapport with them. Do search on this site; you will get a lot of ideas on employee engagement.
Regards