I’m not sure why you imagine that building this at full-grid power levels might take less than a decade, nor why it might be an all-or-nothing proposition given every single gigawatt can be seen as as a (12GWh? I’m not sure but that magnitude) battery system not purchased, but I’ll gladly do the maths.
1) HVDC designs I’ve seen are copper (towers use aluminium because it’s light, IIRC)
2) http://www.necplink.com/docs/Champlain_VT_electronic/04%20L....
Gives 2500mm^2 cross section for a 1 GW cable
3) WolframAlpha says Europe’s electricity production is 410 GW: https://www.wolframalpha.com/input/?i=total+Europe+electrici...
Which means the total conductor cross section needed is ~1 million mm^2 = 1m^2. Ok, this sounds like it’s going to be a lot.
4) Lets put a line across the Sahara to connect all the panels plus connections to the existing EU grid in Gibraltar, Athens, and Milan.
It’s about 3700km from Casablanca to the middle of Egypt: https://www.wolframalpha.com/input/?i=casablanca+to+egypt
Likewise 350km for Gibraltar, 1000 km Awjilah to Athens: https://www.wolframalpha.com/input/?i=Awjilah+to+athens
This gives a total length of about 5000km, if I spec the cable for 100% of EU power going through each cable, which is excessive as I was trying to suggest this as an adjunct to batteries and local PV rather than a total replacement for either: any combination (including none) of transmission and storage only has to cover lower nighttime/seasonal averages).
This gives me a total volume of 5000km * 1m^2 = 5e6 m^3.
5) This is copper, worldwide production of copper is 14.6e6 tons/year, given the density this is indeed 1.4e6 m^3/year and therefore multiple years at current mining.
6) Global aluminium production is 82.6 million tons/year: https://www.wolframalpha.com/input/?i=worldwide+aluminium+pr...
Aluminium is 60% the conductivity of copper; I assume that means I need the conductor to be 1/0.6 times the cross section? Not my field. Assuming that, I want 8.3e6 m^3 aluminium, given the density that’s 22 million tons, so 3 months.
Edit: I forgot Milan!
7) Tataouine to Milan is about 1500 km: https://www.wolframalpha.com/input/?i=Tataouine+to+Milan+
Therefore multiply my mass estimates by 1.3
Edit 2:
410 GW is also 2-2.5 times current global PV installation: https://en.wikipedia.org/wiki/Growth_of_photovoltaics
If you did put enough PV for all of Europe on top of/along side the Casablanca-Egypt line, the PV would need to be about 550m wide: http://www.wolframalpha.com/input/?i=%28410GW%2F%281kW%2Fm%5...
(I only need to care about peak power in this case, not average, hence only the 20% efficiency factor and not including the additional 25% duty factor).