Agree with the above. Is there any service that provides free legal counselling in your area? Some law offices offer free consultation for 30 minutes. Maybe the town/municipality you are in has some free legal consultation service through the city hall? Note that it will be hard to give any advice is there is no pending legal issue. Things to consider are: whose name is on the lease/mortgage? Who pays the bills: whose name is on the contracts with the gas, electric, water, NHK? Are these paid automatically from that person's account, or is there some other arrangement? Same goes for any big assets, like a car. Note all of these down for future reference. Also, does she have access to your bank accounts or credit cards (even though her name is not on them) and vice-versa, do you have access to any of her finances even though your name is not on them. Make a note of these too.
If your intention is to reconcile at some point and remain married, you should tell your wife that, just to have a record that this is your intention/hope. (You don't want to end up in court and have your wife claiming it was you who initiated any separation). I mean, its tough if you are already in an adversarial situation, but I would do it just to be crystal clear. If its just a rough patch that you can resolve with time, then its still good to show her early on that you want to get through this and remain married.
Anyway, my first advice would be to document everything - even if it is from your own (admittedly) biased point of view. In addition to the legal/finanical bits above, just make a simple narrative that a lawyer can look at. Something like;
Background: Wife and I married on Jan 1st, 2020. Child born Jan 1st 2021. All three living in apartment registered in her name (contract is in her name) for rent of 100,000 yen per month. I paid down payment, and pay for 75% of rent from my wages at XXX trading company. All documentation for apartment, electricity, water, gas, is in her name, but all bills are paid from my bank account at MUFJ, Yokohama Branch.
March 1st Wife and I argued over finances. Became difficult to live together.
March 24th 12:00. Wife asked me to move out. Tried negotiating, but rather than escalating, I agreed to move out temporarily, but told her I did not want to divorce.
March 27th 8:00. Moved to Sakura-cho.....etc..
Lastly, if you are here on a spouse visa, you have a possible residence issue if you get divorced. If you are employed, and are here on a work visa, you have much less to worry about.