It can be difficult to find Grass Fibres in Dragon Quest Builders 2 because it's not explained how to obtain it, but it's essential later in Chapter 1. Fortunately, the player can get it as soon as they start in Furrowfield.
The wild Cattails found south of Furrowfield provides players with Grass Fibre.
On the map below, you can see that there is a Bog south of the town of Furrowfield. Sugar Cane Seeds can be found there, so players are required to visit The banks of the Bog.
The player will receive one Grass Fibre for cutting a wild cattail. Wild cattails are commonly found in puddles of water, usually on the shallow points, everywhere in the bog. Fortunately, they are seldom used on the first island, so it is unnecessary to stock up beyond 25-30.
Players can also fast travel to this point if they already have the seeds they need, thanks to a nearby teleporter. If you already used the dog to locate Sugar Can Seeds, it is available for interaction with this object.