How much will a terrible freshman undergradate year affect academic future?
Your older work is far less important than what you have done since. If you have turned it around and people are willing to attest to that in letters of recommendation the first year will likely hurt you very little. I can't say not at all, but not as much as you fear.
For future stuff, focus on the future and on what you have learned enables success there. You are far from alone in this and many students have a slow start. It is good actually, that you found a way to do better. People may well recognize that.
You may have to answer questions in an interview about your first year, so expect that.

Note that the past is past and you can't change it. What you can do now is work so that the past is irrelevant to the future. Make sure you haven't missed any essential knowledge from the early years. Work closely enough with current faculty (projects, research, ...) that they will enthusiastically support your next steps.