Three-Heart Dance Partner lets you dance with a villager at the Flower Dance with three hearts instead of four, so it's achievable in the first year.

Install

Install the latest version of SMAPI.
Unzip the mod folder into Stardew Valley/Mods.
Run the game using SMAPI.

Use
The mod works automatically once installed. If you have at least three hearts with an NPC, they'll accept at the Flower Festival if you ask them to dance.

(You can change the number of hearts needed.)

Formula
The Flower Dance happens on spring 24, which gives you 23 days to get three hearts (750 points) with the NPC of your choice. To achieve that in year one, you can talk to them every day (+20 points/day) and give them two liked gifts per week (+45 points/gift). That gives you (23 days × 20 points) + (4 weeks × 2 gifts × 45 points) or 820 points. You can use Lookup Anything to see your exact friendship points with an NPC.

Compatibility
Compatible with Stardew Valley 1.5.5+ on Linux/macOS/Windows, both single-player and multiplayer.

See also