No, when you request the token you need to have your management API as the audience.
For example:
const response = await axios({
method: 'POST',
url: `https://{tentant}.auth0.com/oauth/token`,
headers:{ 'Content-Type': 'application/json'},
data:{
client_id: <client_id obtained from newly created API>,
client_secret: <client_secret obtained from newly created API>,
audience: `https://{tentant}.auth0.com/api/v2/`,
grant_type: "client_credentials"
}
})
The audience param defines what resource is consuming the token. Your custom API (example-API) has nothing to do with this transaction.