A lot of people seem to be struggling with coins early on so here's what worked for me.
Day 1-3: Focus on foraging. Pick up every shell on Blue Beach and every mushroom in the forest areas. You can easily grab 40+ shells per day just running along the coastline and they add up fast.
Day 3-5: Get your fishing rod upgraded at the Workbench. Upgrade from Wooden Rod to Chrono Rod as soon as you can. Ocean fishing near Half-Moon Bay gives you decent catches like Red Porgy and Spinefoot that sell well.
Day 5-7: By now you should have your Junior Farmer certification. Plant potatoes since they grow fast and sell well. With sprinklers from the Crafting Station you won't need to water manually.
Bonus: Once you unlock the Jam Maker, turn your extra fruit into jam. Processed goods sell for way more than raw fruit.
By end of week 1 I had a solid amount saved up. Enough for the first Land Expansion and a coop for chickens.