If you'd prefer to watch the walkthrough of the quest you can do that in this video but below that I have listed all the actions and times they take so you can make your way through the quest and unlock the prizes in the most efficient way possible. Hope it helps!
With thanks to EA/Firemonkeys for the early access preview build.
Send Sims to the park
Talk to the professor 30 seconds
Consider helping (park bench) 41 minutes
Agree to help (professor) 2 hours 15 minutes
Sleep on some ideas (bed at home ) 3 hours
Sanity check ideas (PC) 1 hour 26 minutes
Watch talking tech on TV 3 hours 55 minutes
Discuss ideas (with professor in park) 3 hours 15 minutes
Install HANS (PC) 1 hour 44 minutes
Inspect computer 3 hours 10 minutes
Report to professor 4 hours 35 minutes
Discuss solution with professor 5 hours 55 minutes
Get clarity from the professor 4 hours 55 minutes
Find parts (20 total) Fridge, sink, shower 2 hours 30 mins, laptop 2 hours 20 minutes (I had random part amounts between 4+6) espresso machine and TV not searchable.
Make transmitter (front lawn) 6 hours 26 minutes
Plug in transmitter (PC) 7 hours 30 minutes
REWARD. Milestone prize: 5 social points.
Device booting. Wait 1 day 23 hours
Vent to another Sim 1 hour 15 minutes
Consider design (couch) 3 hours 15 minutes
Discuss power source with 5 Sims 3 hours and 55 minutes (can be done with just two but best to be done with multiple at the same time)
Read Geological records (bookshelf) 5 hours 55 minutes
Dig for Dimlite (park) 5 hours 30 minutes
Add Dimlite (PC) 1 hour 8 minutes
Respond to voice (PC) 4 hours 10 minutes
Cold shower 3 hours 15 minutes
Speak to HANS (PC) 2 hours
Talk about ice cream (PC) 3 hours 50 minutes
Take selfie (PC) 1 hour 50 minutes
Befriend HANS (PC) 2 hours 40 minutes (Do 8 times, can be done with one sim but more productive with 8 at same time)
Teach HANS (PC) 4 hours 10 minutes
Confront HANS (PC) 3 hours 50 minutes
Call whisperer hotline (phone) 4 hours 55 minutes
Discuss problem with Susan 6 hours 5 minutes
REWARD. Milestone prize: 15 social points.
Wait for Susan for 4 days and 23 hours
Discuss solution (Susan) 5 minutes
Find parts (50 total) Laptop and bed 2 hours 20 minutes, Dining chair, bookshelf, bathroom sink, toilet and couch 2 hours 30 minutes (I had random part amounts between 5+7) Phone, lamp, wardrobe, table, plant and trash can not searchable.