I understand that zero economic profit does not equal to zero accounting profit. It means that every resource that goes into the production is perfectly utilized considering alternative uses in the economy and nothing more. If every company in the economy is earning zero economic profit, can they contribute to real economic growth? (Ceteris paribus)
The standard measure of the size of an economy is total income. Profit is just one type of income (accruing to owners of firms). Wages that accrue to the workers in a firm can increase, which can be taken from the profit of the firm. In that way, income from other sources can continue to increase even though firms earn zero profit.
Other sources of income are rent (from land), and interest (from owning productively-used capital), but I'll stick to wages to keep it simple.
So, you can see that there are different markets at play—the labour market, the market for land, and the market for capital (or input goods). The important thing is that one does not, for example, simply take profit away from firm owners and give it to labourers. It must be a result of equilibrium in these markets. So, for example, if equilibrium in the labour market determines that wages for that sector must be high (e.g. due to scarcity of skills or an abundance of demand for those skills), then that high wage is just a cost of production that firms in that sector must swallow, in order to produce in that sector. Even though competition drives profits down to zero, all the other firms in that sector will also be having to pay the market wage rate.
I'm answering your question in a highly theoretical fashion, but then again, zero economic profit across the economy is a highly theoretical situation itself.
To clarify, I'm arguing that aggregate income can increase through other forms of remuneration, even though profits stay at zero.
If you had a ceteris paribus clause that said these additional income sources remained the same, then economic activity would remain constant (i.e. growth would be zero). Take note that even if the wage rate (or interest rate or price of renting land) remained the same, an increase in the number of firms entering the market would increase economic activity. So, this ceteris paribus clause is not so much talking about the rate of remuneration remaining constant, but rather the aggregate level of income from other sources remaining constant.