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The amount of time it takes for the first shoots to poke through the soil depends on the air and ground temperature. Cooler temperatures may slow the plant’s growth. If there's still no sprout after 3 weeks, carefully dig up the bulb to inspect it for rot. Cut off any bad spots, then plant it again. Since elephant ears are tropical plants, they require a lot of moisture. Water the plant as close to the soil as possible underneath the foliage so you avoid getting the leaves wet. It’s best if the plant is dry at night to prevent diseases.  Never let the plant dry out between watering. This stresses the plant. Drooping leaves signal that the plant needs more water. Elephant Ear plants are heavy feeders and flourish in fertile soil. A slow-release fertilizer keeps your plants fed by gradually releasing nutrients in the soil to promote steady, consistent growth. It also requires less maintenance on your part.  Look for a fertilizer that’s high in nitrogen. Nitrogen helps the plant produce chlorophyll, which gives the leaves that gorgeous green color. Mix compost matter or manure into the soil for extra nutrients. This will encourage new leaves to grow and keep your garden looking lively. Use garden shears to remove the bad leaves as close to the bulb as possible without cutting the bulb.  Wear gloves when you’re trimming the leaves if you have sensitive skin. Their are certain compounds in the leaves that can irritate your hands. A lot of brown or yellow leaves are a sign the plant is either not getting the right amount of sunlight or isn't getting enough water.

Summary:
Wait 1 to 3 weeks before expecting your first sprout. Water the plant in the morning at the roots to keep the soil moist. Fertilize your plant once a month with a slow-release fertilizer. Trim away faded or browning leaves as needed.