Controlling all units/powers, Russia can own 34 centers by after Spring 1905. It's impossible to do it sooner because you can only generate 4 units per turn, so you can't have 17 units until the beginning of Spring 1905.
There are many ways it can work. Here's one of them:
SPRING 1901
R Sev-Arm, War-Gal, StP-Fin, Mos-StP, War-Sil
T Ank-Bla, Smy-Syr, Con-Smy
A Tri-Adr, Bud-Ser, Vie-Tyr
G Kie-Hel, Mun-Bur, Ber-Mun
I Ven-Tri, Rom-Tus, Nap-Tys
F Bre-MAO, Par H, Mar-Spa
E Edi-NWG, Lon-Nth, Lvp-Wal
FALL 1901
R Arm-Ank, Sil-Ber, Fin-Swe, StP-Nor = +4 from Nor, Swe, Ank, Ber (build four armies). Owns StP, War, Mos, Sev, Nor, Swe, Ank, Ber (8).
T Bla H, Syr H, Smy-Arm = -1 from Ank (disband Arm). Owns Con, Smy (2).
A Adr-Ion, Ser-Alb, Tyr H = -1 from Tri (disband Tyr). Owns Vie, Bud (2).
G Mun-Ruh, Bur H, Hel H = -1 from Ber (disband Ruh). Owns Kie, Mun (2).
I Tys-Wes, Tus H, Tri H = +1 from Tri (build F Nap). Owns Ven, Rom, Nap, Tri (4).
F Spa H, Par H, MAO-NAO = +1 from Spa (build F Bre). Owns Bre, Par, Mar, Spa (4).
E NWG H, Nth H, Wal H = even. Owns Edi, Wal, Lon (3).
Unowned: Hol, Bel, Por, Tun, Rum, Bul, Ser, Gre, Den (9)
SPRING 1902
R Ank-Con, Sev-Rum, Mos-Sev, Nor-Lvp, StP-Nor, Swe-Den, Ber-Kie, War-Sil
T Bla H, Syr H
A Alb H, Ion H
G Bur H, Hel H
I Wes H, Tus-Pie, Tri-Tyr, Nap-Tys
F Bre-MAO, NAO C Nor-Lvp, Spa-Gas, Par H
E Wal H, Nth H, NWG C Nor-Lvp
FALL 1902
R Con-Bul(sc), Sev-Con, Rum-Ser, Sil-Mun, Kie-Hol, Den H, Lvp H, Nor-Spa = +8 from Bul, Con, Ser, Mun, Hol, Den, Lvp, Spa (build four armies). Owns StP, War, Mos, Sev, Nor, Swe, Ank, Ber, Bul, Con, Ser, Mun, Hol, Den, Lvp, Spa (16 centers but only 12 units).
T Bla C Sev-Con, Syr H = -1 from Con (disband Syr). Owns Smy (1).
A Alb H, Ion H. Owns Vie, Bud (2).
G Bur H, Hel H = -1 from Mun (disband Bur) . Owns Kie (1).
I Pie-Tyr, Tys H, Wes H, Tyr-Boh = even. Owns Ven, Rom, Nap, Tri (4)
F Gas H, Par H, NAO C Nor-Spa, MAO C Nor-Spa = -1 from Spa (disband Par). Owns Bre, Par, Mar (3)
E NWG C Nor-Spa, Wal H, Nth H = -1 from Lvp (disband Wal). Owns Lon, Edi (2).
Unowned: Por, Tun, Rum, Bel, Gre (5).
SPRING 1903
R Sev H, Con H, Bul-Aeg, Ser-Tri, Mun-Bur, Hol-Bel, Den-Hel, War-Gal, StP-Nor, Mos-StP, Lvp-Yor, Spa H
T Bla H
A Ion H, Alb-Ser
G Hel-Kie
I Tyr H, Boh-Sil, Tys C Gas-Tus, Wes C Gas-Tus
F NAO H, Gas-Tus, NAO C Gas-Tus
E NWG H, Nth H
FALL 1903
R Sev-Con, Con-NAf, Aeg C Con-NAf, Nor-Gas, StP-Nor, Gal-Boh, Tri-Ven, Bur H, Bel-Pic, Hel-Hol, Spa H, Yor H = +1 from Ven. Build 4 armies. Owns StP, War, Mos, Sev, Nor, Swe, Ank, Ber, Bul, Con, Ser, Mun, Hol, Den, Lvp, Spa, Ven (17 centers but only 16 units).
T Bla C Sev-Con =even. Owns Smy (1).
A Ion C Con-NAf, Ser-Bud = even. Owns Vie, Bud (2).
G Kie-Bal = even. Owns Kie (1).
I Boh-Sil, Tyr H, Tys C Con-NAf, Wes C Con-NAf = -1 from Ven (disband Tyr). Owns Rom, Nap, Tri (3).
F NAO C Nor-Gas, NAO C Nor-Gas = even. Owns Bre, Par, Mar (3).
E Nth H, NWG C Nor-Gas = even. Owns Edi, Lon (2).
Unowned: Por, Tun, Rum, Bel, Gre (5).
SPRING 1904
R Nor-Cly, StP-Liv, Con-Alb, Aeg C Con-Alb, Sev-Arm, Boh-Tyr, War-Sil, Mos-War, Yor H, Hol H, Pic H, Bur H, Gas H, Spa H, Ven H, NAf H
T Bla H
A Bud-Gal, Ion C Con-Alb
G Bal H
I Sil-Pru, Tys H, Wes H
F NAO H, MAO H, Tus H
E NWG C Nor-Cly, Nth H
FALL 1904
R Sil-Boh, War-Gal, Alb-Apu, everyone else H = even. Build army Sev. Owns StP, War, Mos, Sev, Nor, Swe, Ank, Ber, Bul, Con, Ser, Mun, Hol, Den, Lvp, Spa, Ven (17 centers and now 17 units).
T Bla H = even. Owns Smy (1).
A Ion C Alb-Apu, Gal-Ukr = even. Owns Vie, Bud (2).
G Bal H = even. Owns Kie (1).
I Wes H, Tys H, Pru H = even. Owns Rom, Nap, Tri (3).
F NAO H, MAO H. Tus H. Owns Bre, Par, Mar (3).
E NWG H, Nth H = even. Owns Edi, Lon (2).
Unowned: Por, Tun, Rum, Bel, Gre (5).
SPRING 1905
R Sev-Rum, Arm-Smy, Aeg-Gre, Apu-Nap, Ven-Rom, Tyr-Tri, Boh-Vie, Gal-Bud, Liv-Kie, Bur-Par, Hol-Bel, Pic-Bre, Gas-Mar, Spa-Por, Yor-Lon, Cly-Edi, NAf-Tun = +17. Owns 34 centers.
T Bla H = -1 from Smy. Owns zero.
A Ukr H, Ion H = -2 from Vie, Bud. Owns zero.
G Bla C Liv-Kie = -1 from Kie. Owns zero.
I Wes H, Tys H, Pru H = -3 from Rom, Nap, Tri. Owns zero.
F NAO H, MAO H, Tus H = -3 from Bre, Par, Mar. Owns zero.
E NWG H, Nth H = -2 from Edi, Lon. Owns zero.
Unowned: none.