You ALSO, need to teach your Eldest child, about baby safety.
I did that, when I had my 2nd child and my eldest was 3-4 years old.
I EXPLAINED to my Eldest daughter, what a baby is, how they are, how they can get hurt or choke, what is dangerous for her baby brother, etc.
She understood. And understood well. Even if she was only 3-4 years old.
So in addition to making the home baby proofed/safe, you also explain to your Eldest child, why.
And still always supervise.... the baby.
I baby proofed my home, per the youngest child.
And then we and my eldest, just adapted to that.
Being aware of safety and choking hazards. Until my youngest, my son, was old enough.
I never banished my Eldest child, just because her brother was a baby.
But you still have to baby-proof.
OR... get a Super-Yard play yard, for baby to be in.
And sequester the baby. When you are busy cooking etc. or in the bathroom.
Don't make the Eldest child feel 'punished' just because the sibling is a baby.
The ENTIRE family, has to practice baby safety and around the home.
Not only the Eldest child.
You cordon off the baby.... via a play-yard or play-pen.
To this day, even if my youngest is now 4 years old, my Daughter... will tell me things like "Mommy, I found this small plastic thing, brother can choke..." and she puts it away up high.