Can I visit my British husband in the UK on a tourist visa for 6 months before applying for the spouse visa?

My understanding is that a requirement of the spouse visa is that the British citizen needs to show at least 6 months worth of payslips to prove income above £18,600.

I am a US citizen currently living in the US, while my British husband is living in the UK. He does make the minimum £18.6k but right now he cannot show 6 months consecutive payslips, as he was just recently visiting me in the US for 3 months. So since he's been back in the UK, he has only 2 months in a row to show and he will will not make it to 6 months since he needs to come back to the US for the birth of our first child. At that point, he will have worked for 5 months so he'll just miss it and will need to start over from 0 once he returns to the UK, so we can qualify to apply for a spouse visa for me.

My question is, am I allowed to come and stay with him (and our child) for 6 months on a visitor's visa while he is working? After the 6 months are up, I would go back to the US and apply for the spouse visa.

My concern is that immigration officials will not believe I intend on leaving the country after 6 months, especially if I have a British husband and child there and am not working myself. How can I prove that I am actually going to leave besides showing a return ticket, because I doubt that will be enough? I don't want to be denied entry into the country.Will it make a difference if we all travel together at the same time or if he goes back ahead of me and I come along later with the child? Will they be suspicious if I am entering on a US passport and my child has a UK passport?

We do plan on applying for the visa, but in the meantime, we would like to be together with our firstborn while we wait to qualify for it.

It can be difficult, and maybe you should try and apply for visitor visa in USA first, explaining that you are going to come back. But still no guarantee.
To prove - you will have to show strong ties, like your own house, your job in USA etc.
On the border control they can ask you why you come and for how long, and to turn you away, because your real intention is living in the UK but not visiting. Also I wouldn’t recommend lying in your application or on the border regarding your intentions, can be used against you in future.

Be very very careful with coming to the UK to stay with your family on a visitor visa. I was detained at the airport and put into an immigration detention cell for more than 10 hours when I attempted it and I only came for 2 weeks. They won't allow you full 6 months for this and you will have to convince HO you will leave and apply for a proper spouse visa.