Quality is initially capped at 100. You need to unlock higher caps (300, 600, 999) in the skill tree. Increase the cap to 300 at least before considering high-quality synthesis. To speed up unlocking the skill tree, go for the skills that increase SP gained from synthesis first (+10/20/30%). Gathering tool recipies and gathering related skills are also very important (gathering rank, gathering quality, gathering quantity), as well as Synthesis Quantity.

Note: 300 quality synthesis is locked behind analyzing 2 ruin fragments, and 600 quality synthesis behind analyzing 10 ruin fragments

Keep any (Gunpowder) / (Fuel) ingredients with quality/quality+/high quality traits.
Relevant ingredients: Beehive, Crimson Ore, Scrap Paper, Flammable Bark, Natural Oil, Fuel Coconut, Unknown Egg, Werder Nut, Fluffy Wool, Dry Grass, Fertile Soil

Keep any ingredient with quality++, this is very rare early game (there's some in a chest in the forest of beginnings, you can transfer those to red neutralizer via wind shoes later on).

When crafting, always pick quality traits even if you didnt unlock the trait slots. (you can unlock the trait slots with rebuild if needed)

Red Neutralizer feeds into itself via Add (Gunpowder) and Add (Fuel). Use this loop to create a 300 quality red neutralizer with [Quality] Lv15, [Quality+] Lv30 and [High Quality].

Note: Zettel is a 250 SP unlock

Use the high quality Red Neutralizer to create 300 quality Zettel with [synth quantity +1].

Note: Recipe Morph is a 500 SP unlock

You need to unlock Gathering rank 2 to gather Foamy Water, and unlock Traveler's Water Orb through the Zettel Recipe morph.

Now you can use Zettel to make Traveler's Water Orb, and Traveler's Water Orb to make more Zettel.

Note: woodcutter's axe is locked in the skill tree until you analyze 1 ruin fragment.

You need a Woodcutter's Axe capable of getting rank 2 ingredients (capable chopping) for the next part. Use this axe to gather coral stone or riverstone.

Use these new ingredients to add the lightning element to your traveler's water orb.

Morph a high quality Delphi Rose Incense from the Traveler's Water Orb.

Make a 600 quality Crystal element (morph from mixing oil - alchemy paint - spirit bottle).

Make a 999 quality Philosopher's stone (morph from crystal element).

Make maxed seeds.