There are a few ways to help a parent with daily money matters if your parent is reluctant to name you power of attorney.
Start by helping with tasks that don't require that you be your mom's power of attorney, such as helping her sort the mail to separate the junk mail from the bills, helping ensure bills get paid, helping create a budget and monitoring spending.
Take advantage of technology, such as the Carefull app. You can link your mom's accounts to the app (with her permission), and the app will monitor those accounts 24/7 for missed or late payments, duplicate payments, changes in spending, unusual purchases, signs of fraud. You'll get alerts if something might be wrong. The app gives you view-only access to your mom's accounts. So she might feel more comfortable knowing that you won't be able to make any transactions.
Even though you think your might be reluctant to name you power of attorney, please do talk to her about it. She must be mentally competent to name you power of attorney. So if something were to happen and she was no longer of sound mind, you'd have to go through the court system to be named her conservator. You can simply tell her to have the document drafted now. She can hang onto it but let you know under what circumstances you would be allowed to access it and start acting as her power of attorney. (You need the actual document to present to her financial institutions -- you can't simply tell them you are her POA.)