To help get rid of your toddler's cold fast you can use a saline solution to clean out the toddler's nose.
That will help the toddler be able to breathe better and help speed up the cold recovery in the toddler.
Also use a humidifier to add moisture to the toddler's room as humidity helps the toddler breathe better and keeps them from becoming congested.
Allow the toddler to get plenty of rest and try to get them to stay in bed or lay down if they have a cold as that will help them recover quicker.
Make sure the toddler stays hydrated by giving them plenty of water, juice such as orange juice that contains vitamins.
If your toddler is old enough and they have a sore throat along with the cold you can give the toddler a little bit of honey or some cold medicine that is made for toddlers.
There's not much else you can do to get rid of the cold faster other than the above and waiting it out.
The toddler should recover from the cold virus within a week to 14 days.