Do you mind, if we back up a little? We need some information, to help you get to where you want to be.
IIUC, you are taking the DIY-Build-It-Yourself approach, to save some money... (It is admirable that you would go to such lengths, to bless your child.) So, we need to check out the economics... We also need to consider the needed equipment, your skills and your long-term interest in electronics as a hobby. We'll back into it; here we go...
- What is your long-term interest in the hobby? This project will have many learning curves to climb.
- You will need to own, or have access to, a decent soldering iron and multimeter. Include solder wire, flux and cutters to trim pins, too... We need to know what you have to use.
- You have mentioned some of the parts that you have on hand. Do you have any of the others used in the circuit?
- What soldering and fabrication skills do you have?
What I am getting at is this... If this is a one-off project having only the purpose to provide the synthesizer to your child, there may be easier and cheaper solutions than developing/modifying a circuit from scratch. There will be a great amount to learn with each facet of the construction. You will be investing time, energy and frustration, but the rewards will be so very great... The money savings of doing it yourself will likely be lost, if you have to buy much equipment.
An intermediate step might be to build a known kit. That will be a little more upfront money, but tons less development effort and failure/redo costs. Since your daughter is just getting started, a clone device might do okay... Meaning Ebay, Banggood, etc. If you want something more reliable, there are OEM synth kit providers.
I am trying to make sure that you have a positive experience. We want you to have fun and catch the same electronics bug that we relish. Give us this information and we will be much better positioned to help you be successful. And, if you are just wanting to do this one project, that's fine, we'll still help.
Oh, the power supply that you have... That is a switch-mode power supply, which can be electronically "noisy." Your project involves creating frequencies. The two don't mix so very well... I would suggest a different supply, IMHO. Just good old batteries?
https://www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=atari+punk+console+kitThe Jameco kits are known.
https://www.ebay.com/sch/i.html?_from=R40&_trksid=p2334524.m570.l1312.R1.TR0.TRC0.A0.H0.TRS2&_nkw=atari+punk+console+kit&_sacat=0&LH_TitleDesc=0&_sop=15&_osacat=0&_odkw=atari+punk+console&LH_TitleDesc=0