You can check whether you have followed the below steps properly.
On the left panel of the configuration, section click on Sales > Shipping Methods
Then, Scroll down to Free Shipping.
If you want to edit you can clear ‘Use System Value’ checkbox.
- Enabled: Select yes
- Title: Enter the name of the shipping method this will be displayed in the checkout page.
- Method name: This will be shown to the user at checkout.
- Minimum Order Amount: Order has to be above this value then only free delivery will be available
- Displayed Error Message: Error message this will available when this order is not available.
- Ship to Applicable Countries: Since it is free delivery allows it only to your country.
- Ship to Specific Countries: Select the countries you want to deliver to.
- Show Method if Not Applicable: If you want to show free shipping method even when it is not available to select yes
- Sort Order: Give 0 if you want to show free shipping as the first option
Save this configuration.
Or you can also use extensions like https://marketplace.magento.com/storepep-storepep-shippingcalculator.html
When set free shipping this extension will automatically select the cheapest and among them the fastest shipping carrier service.