One source earlier than R. Hayyim Valozhiner is Ritva (Rosh HaShana 16a) who states precisely this:
וכל תורה שבע"פ רמוזה בתורה שבכתב שהיא תמימה
The entire Oral Law is hinted to in the Written Law, which is perfectly complete.
Another source which states this (before the 18th century) is the Shelah (Tol'dot Adam R'mazei HaOtiot Lahatimat HaHakdama):
כל תורה שבעל פה רמוזה בתורה שבכתב
The entire Oral Law is hinted to in the Written Law
A broader statement, that everything is hinted to in the Torah is made by R. Eleazar Rokeah in Sefer HaShem (p. 43):
ללמדך כי כל דבר רמוז בתורה אלא שנעלם מבני אדם
To teach you that everything is hinted to in the Torah, but it is hidden from people.
A similar sweeping statement is made by R. Nattan of Clermont (late 13th century) in his commentary to the haggada (published in Moriah 257-9 (5759)):
שכל הענינים רמוזים בתורה
All things are hinted to in the Torah.
The context is the praise of "barukh hamakom" praising God for giving the Torah, in conjunction with the statement that the Torah hints to the responses to four types of children.