Sure you can! Galactic coordinates have the same origin as other J2000.0 systems; the solar system barycenter (center of mass). This is very close to the Sun, usually but not always inside the Sun, because the larger planets, especially Jupiter, pull it around a little bit. You can read a little more here for example, and also read @zephyr's excellent answer.
At first you might ask why the origin of the galactic coordinates isn't the center of the galaxy. I'm pretty sure that the answer is that we don't know where that is! We'd have to know the masses and locations of everything, and of course since most of the galaxy's mass is dark matter we're not going to know where the center of mass is any time soon.
However, the XY plane of the galactic coordinates has been chosen for now, based on an estimate of the Galaxy's apparent equator. Since it's a different plane than our solar system's plane, otherwise known as the ecliptic, the coordinates will be different even though the origin is the same.
Since galactic coordinates are centered near the Sun, the distance of our position from the origin will still be about 1 AU (150,000,000 km).
Below I wrote a little script in Python using the easy-to-use Skyfield python package. At the moment that I've run the program , the coordinates are:
time (JD): 2458099.18846
time (UTC): (2017, 12, 11, 16, 31, 23.049599826335907)
latitude (degs): 41.42
longitude (degs): 2.15
galactic (km): [ -1.46347711e+08 -2.89156773e+06 -2.34254700e+07]
barycentric (km): [ 2.69276456e+07 1.33751808e+08 5.79665590e+07]
and just for fun...
galactic latlon (degs): [-9.0922867698877123, 181.13191434418721]
Here is the Python script:
import numpy as np
import matplotlib.pyplot as plt
from skyfield.api import Loader, Topos
load = Loader('~/Documents/SkyData')
planets = load('de421.bsp')
earth, sun = planets['earth'], planets['sun']
ts = load.timescale()
tnow = ts.now()
tmonth = ts.utc(2017, 12, range(1,31))
topo = Topos(latitude_degrees=41.42, longitude_degrees=2.15)
position = earth + topo
print "time (JD): ", tnow.tt
print "time (UTC): ", tnow.tt_calendar()
print "latitude (degs): ", topo.latitude.degrees
print "longitude (degs): ", topo.longitude.degrees
print "galactic (km): ", position.at(tnow).galactic_position().km
print "barycentric (km): ", position.at(tnow).position.km
print "and just for fun..."
print "galactic latlon (degs): ", [x.degrees for x in position.at(tnow).galactic_latlon()[:2]]