If you don't already know who Big is I'm gonna put his character bio from his first game in Japanese here. And Sonic Channel for safe keeping.

Sonic Heroes:

Big the Cat (18 y/o)

A giant cat who lives a carefree life deep in the jungle with his best friend, Froggy. Fishing is his hobby, and he always carries his fishing rod. He is gentle but strong.

He has a very laid-back personality and speaks in a relaxed manner, but when it comes to his friends, he works very hard. 

When his friend Froggy is kidnapped (?), he sets out to look for him again.

Sonic Channel: 

A laid-back, easygoing, and carefree giant cat.

His hobbies are sleeping, eating, and lure fishing. 

He’s gentle-hearted yet strong.

He enjoys a relaxed life in the great outdoors with his beloved friend Froggy, but steps up when his friends are in trouble.

For a reference of the voice I want you to imitate here's a playlist with all Sonic games in Japanese. Sonic X in Japanese is also a good reference.

Solebinku's Personal Direction:

For big its easy sound as relaxed and deep as you feel needed. His voice is a male calm kind of voice that sounds super relaxed, almost to the point of sounding slow. He's a chill guy he never really shows any emotion he's kind of emotionless it's funny. He is also Tenor that is so relaxed he's a little bit of a bass.

Follow the Japanese to the point where you can find that relaxed flow. You'll definitely be having Lazy Days after that.

Game Cutscenes:

https://youtube.com/playlist?list=PLhnIPa8XAn7x6g8UvkO0UaiTHtK-VBUbd&si=gTudY2rorUzd7vGB

General Big voice lines.

https://youtu.be/MXQarSeEL2I?si=7vplPsNj3RzMFbXE

https://youtu.be/-0mSw4CeICk?si=kari0Jxsufg-8Rq-

If you want to learn more about the character I made a video for him on my YouTube channel:

(Did not make yet sorry...)