Your sentences sound like a strange re-mix of a Ke$ha song... anyway
I wake up in THE morning when the alarm clock rings. I started THE day (although today isn't incorrect, as such) with a cup of coffee and birds were singing.
i start today with a cup of coffee
Today is the past for the future.
Make history for the future.
I wake up in ther morning
When the alarm clock rings
I started today with a cup of coffee
And the birds were singing