The short answer is of course, yes. The long answer is that each child progresses at his or her own pace. It's tempting to push kids to concepts we think they should learn, but if they're not ready, you and your child will just end up frustrated. You don't want to send messages that learning = frustration. So, if you try something and it doesn't go over well, give it a couple of months and try again in a slightly different way.
Here's some things you can do to foster early color knowledge.
1. Point out colors in everyday. When you go out for a walk, or are driving in the car, notice the colors. Fall is an especially fun time to look for colors. "Wow, look at that tree! It has lots of leaves. Lots of red leaves!" Or "Look at that car. Did you see the yellow car?" Notice their clothing and say, "You're wearing red today. Look at your red pants!"
2. Look for colors in picture books. There are many books out there specifically for learning colors, but you can also point out colors in any well-illustrated book. One of our favorite shapes and colors picture book is called Color Zoo by Lois Ehlert. The shapes are actually cut out of pages so the animals transform as you turn the page. Lois Ehlert is one of my favorite author/illustrators for toddlers and preschoolers.
3. Introduce just two contrasting colors to start. We like starting with red and blue. Many young kids are drawn to the color red. We use pom poms (cheap and fun) and bowls that I painted to sort by color. But you can just put down red and blue construction paper or anything on hand. Then see if the child can distinguish the colors. Talk to them during the activity. Repeat the color words as they hold each color, "where does the red one go?"
If you're feeling brave, let them use finger paints. You can commentate as they paint. "Look at the red. You're using red. Ooh, now you have blue. Is the blue fun to use?" If might feel a little strange, but your words are teaching and reinforcing the colors.
Here we took pony beads and matched them to a feather or chenille strip. This was also a great fine motor skill.
4. Affirm their efforts. Your encouraging voice is more powerful than you know. This will associate learning colors with your positive voice and encouragement and will reinforce their efforts. I cringe just a little when people say "No!" in that sort of are-you-kidding-me? voice. If they sort an item wrong, wait. Don't say anything. You might be surprised at how often they will self-correct.
Don't forget to have fun. If you are mess-adverse there are plenty of things you can do to teach colors without making a huge mess. Here are some more ideas you might enjoy trying. They're simple and you don't need elaborate supplies to do them.