Polygon and Avalanche are two different networks, so to transfer assets one must use a cross-chain DEX or bridge. These platforms let you seamlessly move stablecoins from EVM-compatible networks like Polygon to Avalanche, Ethereum, Fantom, and many others. Some of the larger protocols that can move assets from Polygon to Avalanche are Synapse, AnySwap, or Elk Finance. These allow the swap of USDC, USDT, or DAI from Polygon to the Avalanche C Chain.
If choosing to use the official Avalanche Bridge, the bridge only bridges the Ethereum and Avalanche Network. In this situation, one would need to move their Polygon assets to the Ethereum network BEFORE using core.app/bridge to move the Ethereum assets over to the Avalanche Network.
Note: Not all Polygon assets can exist on the Avalanche network.