Just research/build, replicator tier 1, water pump, water purifier and greenhouse, don't waste time researching anything else, ONLY go to warehouses don't go to houses.
It's really important to shelter be clean 80% to 100% give you +4 morale every day.
1 day as leader: go to 2 warehouses to get resources, assign to research water purifier and greenhouse and let Ai researching. Set in Rules menu 8 foods for each survivors and 80 water, you have a lot of resources in the start and you get more morale.
2 day as leader: go to 2 warehouses again, check if you can build a replicator, water purifier or greenhouse and let Ai build/reseach.
shelter need some clean to let Ai clean the shelter for 3hs-5hs.
3 day as leader: Ai and Mc need some hours resting to get some happy, 80% is enough, Don't leave shelter this day, Assign Mc to rest and help to clean the shelter, set in Rules Menu 4 foods and 40 water or soon you will get low on food/water.
4 day as leader: go to 2 warehouses again, check if you can build a water purifier, greenhouse. research/build water pump,greenhouse or water purifier and let Ai researching/building, assign some hours to clean the shelter and when mc return, let he help to clean.
5 day as leader: go to 1-2 warehouses again, assign Mc to help to clean/build or research., research/build water pump,greenhouse or water purifier. keep shelter 80% clean or more and survivors 80% happy or more.
Day 8: now you have Mary to help, research,building and cleaning is faster. Mary is 100% happy so just let her clean/build.
Check the "?" Help menu in the world Map