If you have no information, you can use “uninformative” priors. Those priors aim to bring as little information as possible, but as you already learned from the What is an "uninformative prior"? Can we ever have one with truly no information? thread, the name is a little bit misleading because even such priors bring some information to the model. That is why more modern recommendation would be to pick a weakly informative prior (centered on something, but very uncertain).
On another hand, using a frequentist model does not mean making no assumptions: you may still assume things like Gaussian likelihood, a linear relationship between the variables, or using regularized regression you are using implicit priors on the parameters, etc. Even if you wanted to make as few assumptions as possible and used a nonparametric model, you would be making some assumptions. For example, say that you would pick $k$NN regression that just averages among "similar" observations. Still, you need to decide on a similarity metric to define what "similar" means and you need to somehow pick the hyperparameter $k$. With Bayesian models, you make additional assumptions by choosing priors, but other approaches also make assumptions.
But, can you have truly no information about something? Say a meteor hits the planet Earth and brings us a new virus from space. A Bayesian statistician needs to build a model on it. They know nothing about space viruses. Hopefully, they know a lot about viruses from Earth, many scientists also did a lot of educated guesses on what extraterrestrial life forms could be and how they could be similar or different to the life on Earth, etc. The scientist in fact has a lot of prior knowledge and assumptions that they could use to come up with priors.