You're right, you're missing other ways to get new artifacts. According to Stardew Valley Wiki, artifacts can be acquired in the following ways:
- Using the Hoe on worm tiles. Different parts of the map will drop different artifacts. These locations are much more common in winter.
- Using a Hoe on dirt located within The Mines and Skull Cavern.
- Killing Monsters.
- Fishing for treasure chests.
In case you want a list with the artifacts and their locations, see below or refer to this page:
Dwarf Scroll I
Mines level 1-105 (maybe every level, not confirmed)
Green Slime (Secret Woods)
Dwarf Scroll II
Mines level 40-65
Blue Slime (Secret Woods)
Dwarf Scroll III
Mines level 40+
Lava Bat (Mines Level 81+)
Blue Slime (Secret Woods)
Skull Cavern
Dwarf Scroll IV
Any Monster (Mines)
Using hoe on dirt (Mines level 81+)
Chipped Amphora
Town (4%)
Arrowhead
Mountain (2%)
Forest (2%)
Bus Stop (2%)
Ancient Doll
Mountain (4%)
Forest (3%)
Bus Stop (3%)
Town (1%)
Fishing Chest (Ocean/Secret Woods)
Elvish Jewelry
Forest (1%)
Fishing Chest (?%)
Chewing Stick
Mountain (2%)
Forest (2%)
Town (1%)
Fishing Chest (?%)
Ornamental Fan
Beach (2%)
Forest (1%)
Town (0.8%)
Fishing Chest (River)
Dinosaur Egg
Mine (1%)
Mountain (0.8%)
Fishing chest (Ocean/River)
Rare Disc
Underground Mine (1%)
Fishing Chest (Ocean/River)
Ancient Sword
Forest (1%)
Mountain (0.8%)
Fishing Chest (Ocean/River)
Rusty Spoon
Town (5%)
Fishing Chest (River ?%)
Rusty Spur
Farm (10%)
Fishing Chest (River ?%)
Rusty Cog
Mountain (5%)
Mine ~14 in dirt
Fishing Chest (Ocean/River)
Chicken Statue
Farm (10%)
Fishing Chest (?%)
Ancient Seed
Forest (1%)
Mountain (1%)
Fishing Chest (River)
Prehistoric Tool
Bus Stop (4%)
Mountain (3%)
Forest (3%)
Fishing Chest (?%)
Dried Starfish
Beach (10%)
Fishing Chest (River ?%)
Anchor
Beach (5%)
Fishing Chest (?%)
Glass Shards
Beach (10%)
Fishing Chest (Ocean)
Bone Flute
Underground Mine (2%)
Mountain (1%)
Forest (1%)
Town (0.5%)
Fishing Chest (River)
Prehistoric Handaxe
Mountain (5%)
Forest (5%)
Bus Stop (5%)
Dwarvish Helm
Underground Mine (1%)
Dwarf Gadget
Underground Mine (0.1%)
Ancient Drum
Underground Mine (2%)
Bus Stop (1%)
Forest (1%)
Town (0.5%)
Golden Mask
Desert (4%)
Golden Relic
Desert (8%)
Strange Doll 1
Everywhere (0.1%)
Fishing Chest (?%)
Strange Doll 2
Everywhere (0.1%)
Fishing Chest (?%)
Prehistoric Scapula
Town (1%)
Forest (?%)
Prehistoric Tibia
Forest (1%)
Railroad (?%)
Prehistoric Skull
Mountain (1%)
Skeletal Hand
Beach (1%)
Prehistoric Rib
Town (1%)
Prehistoric Vertebra
Bus Stop (1%)
Skeletal Tail
Underground Mine (1%)
Fishing Chest
Nautilus Fossil
Beach (3%)
Fishing Chest (Ocean/River)
Amphibian Fossil
Forest (1%)
Mountain (1%)
Fishing Chest (Ocean)
Palm Fossil
Forest (1%)
Beach (1%)
Desert (1%)
Trilobite
Forest (3%)
Beach (3%)
Mountain (3%)
Best Answer
I don't think it's possible to completely eliminate trees from the game, but you might have to wait a while. Some things to check: