Perfectly Vectorizing Logos in Ai

[BlueCow]

Hello everyone, I'm new to illustrator and I have found a cool logo image on google and I would like to create a path around it perfectly to be able to then vectorize it and change the colors etc.. So, is there a way to automatically (or not) perfectly reproduce the logo so that I can vectorize it later? I have tried the a few ways, I have tried automatically vectorizing the logo and I have tried to create the path around the logo myself with the pen tool and then using the smooth tool to make it better but it's still has some little imperfections. It would really help me out if you know of a way who could help me to achieve this or get very close it. Thank you for reading and have a great day!

The logo:

[BeachSparklez]

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