How am I supposed to get the R&D tickets to get the first s construct before pity resets to 60?

Basic RnD tickets are farmed from Bounty Missions (150-180 max per week) and Event Missions. And If I remember correctly, first S rank construct needs 40 pulls instead of 60. I'd say, pull 40 times with your BC as it'll take theoretically 55 weeks to pull all 40 using Bounties.