Supposedly, this is the Cross of Father Junípero Serra y Ferrer, O.F.M
The location of the Mission Cross is kept at each Mission as a special place because of the longstanding tradition at the Missions to have Mass there and to have prayers like Benediction and the Breviary for priests, also for meetings with the faithful in the shadow of the prominent Cross.
.The cross has been lost to elements many times but it is always replaced and continues to stand above Venutra.
Exposed to the weather, wood does not hold up well, and over time it becomes decayed, so all of the Mission Crosses have to be replaced from time to time. They might last about 20 to 50 years, depending on the climate and the wood species. If they used teak and oiled it with linseed oil every year it might hold up indefinitely, but teak is not a native wood, and the Missions used materials native to the area, usually. One source says this one in Ventura was erected around WWII, which would make it 70 years old. So that's ancient for a wood cross.
The Ark of the Covenant was made from "setim wood" which is reputably impervious to decay, but apparently that's a very unique species found only in the Holy Land. I've never seen it available in California. There is a very hardy wood from England called lignum vitae
(Latin name) which had long been used in old ships for the seals surrounding propeller shafts; it comes from logs buried in bogs and they say there are no more of this species living, it is extinct. It's unlikely that teak, setim wood or lignum vitae
were ever used for a Mission Cross. Coastal redwood is a possibility because of its resistance to termites (but not impervious), but its strength is not very good so the crossbeam would be subject to fracture at the lap joint, where it intersects the vertical post. They could use railroad tie stock which is typically saturated with creosote for preservation, but that has an offensive odor that would be undesirable. Pressure treated or Wolmanized Douglas Fir would hold up well, but it's greenish in color so for the first 10 years or so it would have to be kept painted to look authentic. The Mission Cross looks more authentic when it appears weathered.
Therefore it is the LOCATION of this Cross that is likely from the founding of the Mission, but not the physical cross itself.