Brute force
The brute force solution is simple, just iterate until the number of digits is at least 1000. We can count the number of digits in a number by turning it into a string and counting its length.
From solution1.py:
def thousandth_digit_fibonacci_number(n=1000):
f1 = 1
f2 = 1
res = 1
while len(str(f1)) < n:
f1, f2 = f2, f1 + f2
res += 1
return res