Suggestions to introduce a 5 month old pup to the whole living room

Hi so our 5 month old wired hair dachshund now sleeps in her open crate in a puppy pen. We live in a appartement but she handles the pen and the alone time pretty wel. Now she is alone 4h, i come in between my break to relief her and feed her for 30-40min and then leave her and then she is alone 2-3h max till my girlfriend arrives from her work. It's with shifts so if she works late it's not more then 4 hours she is alone till i come home.

Now if she is 6 months old we only should feed her twice a day from breeder instructions so then i don't need to come home in my break so she stays alone for longer period at once. I only hqve 30 min but i agreed with my boss till she is 6 months i could stay longer with my dog.

But yeah she grows and matures so we would like to give her more space with babysteps but don't know how to approach this. Also with puppy proof things what to look after. First we thought some kind of baby gate at the kitchen but the problem is the wall where te kitchen starts, it are 2 corners across each other, but they don't overlap so we can't place a babygate between the walls and just a gate with legs we think she would easily push furter.

Any advice on this operation and suggestions? Many thanks in advance!!! 😊