Is there a pythonic way of shifting pandas dataframe cells to the left, while pushing out or overwriting any nan?

I have a pandas dataframe (starting_df) with nan values in the left-hand columns. I'd like to shift all values over to the left for a left-aligned dataframe. My Dataframe is 24x24, but for argument's sake, I'm just posting a 4x4 version. After some cool initial answers here, I modified the dataframe to also include a non-leading nan, who's position I'd like to preserve. I have a piece of code that accomplishes what I want, but it relies on nested for-loops and suppressing an IndexError, which does not feel very pythonic. I have no experience with error handling in general, but simply suppressing an error does not seem to be the right strategy.

Starting dataframe and desired final dataframe:

Here is the code that (poorly) accomplishes the goal.

import pandas as pd
import numpy as np

def get_left_aligned(starting_df):
    """take a starting df with right-aligned numbers and nan, and
    turn it into a left aligned table."""
    left_aligned_df = pd.DataFrame()
    for temp_index_1 in range(0, starting_df.shape[0]):
        temp_series = []
        for temp_index_2 in range(0, starting_df.shape[0]):
            try:
                temp_series.append(starting_df.iloc[temp_index_2, temp_index_2 + temp_index_1])
                temp_index_2 += 1
            except IndexError:
                pass
        temp_series = pd.DataFrame(temp_series, columns=['col'+str(temp_index_1 + 1)])
        left_aligned_df = pd.concat([left_aligned_df, temp_series], axis=1)
    return left_aligned_df


df = pd.DataFrame(dict(col1=[1, np.nan, np.nan, np.nan],
                       col2=[5, 2, np.nan, np.nan],
                       col3=[7, np.nan, 3, np.nan],
                       col4=[9, 8, 6, 4]))

df_expected = pd.DataFrame(dict(col1=[1, 2, 3, 4],
                                col2=[5, np.nan, 6, np.nan],
                                col3=[7, 8, np.nan, np.nan],
                                col4=[9, np.nan, np.nan, np.nan]))

df_left = get_left_aligned(df)

I appreciate any help with this. Thanks!